#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "../../template/template.hpp" // #include "../../math/rational-binomial.hpp" #include "../../math/rational-fps.hpp" #include "../../math/rational.hpp" // #include "../../modint/montgomery-modint.hpp" #include "../../modulo/binomial.hpp" using mint = LazyMontgomeryModInt<998244353>; // #include "../../misc/rng.hpp" using namespace Nyaan; void Nyaan::solve() { { Rational a{4, 3}, b{2, 3}; assert(a + b == 2); assert(a - b == Rational(2, 3)); assert(a * b == Rational(8, 9)); assert(a / b == 2); assert(a.inverse() == Rational(3, 4)); assert(a.pow(3) == Rational(64, 27)); assert((a > b) == true); assert((a >= b) == true); assert((a < b) == false); assert((a <= b) == false); } { Binomial_rational<Rational> C; assert(C.fac(3) == 6); assert(C.finv(3) == Rational(1, 6)); assert(C(4, 2) == 6); assert(C(vi{3, 2}) == 10); } { using fps = FormalPowerSeries_rational<Rational>; { fps f{1, 2, {3, 2}}, g{{1, 4}, 5}; fps h{{5, 4}, 7, {3, 2}}; assert(f + g == h); h = fps{{3, 4}, -3, {3, 2}}; assert(f - g == h); assert(f * g % g == fps{}); assert(f * g % f == fps{}); } { fps e{1, 1, {1, 2}, {1, 6}, {1, 24}, {1, 120}}; fps f = e.pow(10); trc(f); rep(i, sz(e)) { assert(e[i] * Rational{10}.pow(i) == f[i]); } } } // mint と挙動の比較 { auto comp = [&](int i, int j, int k, int l) { rep(b, 16) { int ii = (b >> 0) % 2 ? -i : +i; int jj = (b >> 1) % 2 ? -j : +j; int kk = (b >> 2) % 2 ? -k : +k; int ll = (b >> 3) % 2 ? -l : +l; Rational x{ii, jj}, y{kk, ll}; mint X = mint{ii} / jj; mint Y = mint{kk} / ll; assert(X + Y == (x + y).to_mint(998244353)); assert(X - Y == (x - y).to_mint(998244353)); assert(X * Y == (x * y).to_mint(998244353)); if (Y != 0) { assert(X / Y == (x / y).to_mint(998244353)); } } }; rep(i, 20) rep1(j, 20) rep(k, 20) rep1(l, 20) comp(i, j, k, l); rep(t, 10000) { int lower = t % 2 ? 1 : 32000; ll i = rng(lower, 35000); ll j = rng(lower, 35000); ll k = rng(lower, 35000); ll l = rng(lower, 35000); comp(i, j, k, l); } } // binom, mint と挙動の比較 { Binomial_rational<Rational> C1; Binomial<mint> C2; reg(i, -15, 15) { assert(C2.fac(i) == C1.fac(i).to_mint(998244353)); assert(C2.finv(i) == C1.finv(i).to_mint(998244353)); assert(C2.inv(i) == C1.inv(i).to_mint(998244353)); reg(j, -15, 15) { assert(C2(i, j) == C1(i, j).to_mint(998244353)); assert(C2.P(i, j) == C1.P(i, j).to_mint(998244353)); if (i + j < 20) assert(C2.H(i, j) == C1.H(i, j).to_mint(998244353)); } } } cerr << "OK" << endl; { int s, t; cin >> s >> t; cout << s + t << "\n"; } }
#line 1 "verify/verify-unit-test/rational-number.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 4 "verify/verify-unit-test/rational-number.test.cpp" // #line 2 "math/rational-binomial.hpp" #line 2 "math/rational.hpp" #line 6 "math/rational.hpp" using namespace std; #line 2 "internal/internal-type-traits.hpp" #line 4 "internal/internal-type-traits.hpp" using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 2 "math-fast/gcd.hpp" #line 4 "math-fast/gcd.hpp" using namespace std; namespace BinaryGCDImpl { using u64 = unsigned long long; using i8 = char; u64 binary_gcd(u64 a, u64 b) { if (a == 0 || b == 0) return a + b; i8 n = __builtin_ctzll(a); i8 m = __builtin_ctzll(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u64 d = a - b; i8 s = __builtin_ctzll(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } using u128 = __uint128_t; // a > 0 int ctz128(u128 a) { u64 lo = a & u64(-1); return lo ? __builtin_ctzll(lo) : 64 + __builtin_ctzll(a >> 64); } u128 binary_gcd128(u128 a, u128 b) { if (a == 0 || b == 0) return a + b; i8 n = ctz128(a); i8 m = ctz128(b); a >>= n; b >>= m; n = min(n, m); while (a != b) { u128 d = a - b; i8 s = ctz128(d); bool f = a > b; b = f ? b : a; a = (f ? d : -d) >> s; } return a << n; } } // namespace BinaryGCDImpl long long binary_gcd(long long a, long long b) { return BinaryGCDImpl::binary_gcd(abs(a), abs(b)); } __int128_t binary_gcd128(__int128_t a, __int128_t b) { if (a < 0) a = -a; if (b < 0) b = -b; return BinaryGCDImpl::binary_gcd128(a, b); } /** * @brief binary GCD */ #line 10 "math/rational.hpp" // T : 値, U : 比較用 template <typename T, typename U> struct RationalBase { using R = RationalBase; using Key = T; T x, y; RationalBase() : x(0), y(1) {} template <typename T1> RationalBase(const T1& _x) : RationalBase<T, U>(_x, T1{1}) {} template <typename T1, typename T2> RationalBase(const pair<T1, T2>& _p) : RationalBase<T, U>(_p.first, _p.second) {} template <typename T1, typename T2> RationalBase(const T1& _x, const T2& _y) : x(_x), y(_y) { assert(y != 0); if (y == -1) x = -x, y = -y; if (y != 1) { T g; if constexpr (internal::is_broadly_integral_v<T>) { if constexpr (sizeof(T) == 16) { g = binary_gcd128(x, y); } else { g = binary_gcd(x, y); } } else { g = gcd(x, y); } if (g != 0) x /= g, y /= g; if (y < 0) x = -x, y = -y; } } // y = 0 の代入も認める static R raw(T _x, T _y) { R r; r.x = _x, r.y = _y; return r; } friend R operator+(const R& l, const R& r) { if (l.y == r.y) return R{l.x + r.x, l.y}; return R{l.x * r.y + l.y * r.x, l.y * r.y}; } friend R operator-(const R& l, const R& r) { if (l.y == r.y) return R{l.x - r.x, l.y}; return R{l.x * r.y - l.y * r.x, l.y * r.y}; } friend R operator*(const R& l, const R& r) { return R{l.x * r.x, l.y * r.y}; } friend R operator/(const R& l, const R& r) { return R{l.x * r.y, l.y * r.x}; } R& operator+=(const R& r) { return (*this) = (*this) + r; } R& operator-=(const R& r) { return (*this) = (*this) - r; } R& operator*=(const R& r) { return (*this) = (*this) * r; } R& operator/=(const R& r) { return (*this) = (*this) / r; } R operator-() const { return raw(-x, y); } R inverse() const { assert(x != 0); R r = raw(y, x); if (r.y < 0) r.x = -r.x, r.y = -r.y; return r; } R pow(long long p) const { R res{1}, base{*this}; while (p) { if (p & 1) res *= base; base *= base; p >>= 1; } return res; } friend bool operator==(const R& l, const R& r) { return l.x == r.x && l.y == r.y; }; friend bool operator!=(const R& l, const R& r) { return l.x != r.x || l.y != r.y; }; friend bool operator<(const R& l, const R& r) { return U{l.x} * r.y < U{l.y} * r.x; }; friend bool operator<=(const R& l, const R& r) { return l < r || l == r; } friend bool operator>(const R& l, const R& r) { return U{l.x} * r.y > U{l.y} * r.x; }; friend bool operator>=(const R& l, const R& r) { return l > r || l == r; } friend ostream& operator<<(ostream& os, const R& r) { os << r.x; if (r.x != 0 && r.y != 1) os << "/" << r.y; return os; } // T にキャストされるので T が bigint の場合は to_ll も要る T to_mint(T mod) const { assert(mod != 0); T a = y, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return U((u % mod + mod) % mod) * x % mod; } }; using Rational = RationalBase<long long, __int128_t>; #line 4 "math/rational-binomial.hpp" template <typename R = Rational> struct Binomial_rational { vector<R> fc; Binomial_rational(int = 0) { fc.emplace_back(1); } void extend() { int n = fc.size(); R nxt = fc.back() * n; fc.push_back(nxt); } R fac(int n) { if (n < 0) return 0; while ((int)fc.size() <= n) extend(); return fc[n]; } R finv(int n) { if (n < 0) return 0; return fac(n).inverse(); } R inv(int n) { if (n < 0) return -inv(-n); return R{1, max(n, 1)}; } R C(int n, int r) { if (n < 0 or r < 0 or n < r) return R{0}; return fac(n) * finv(n - r) * finv(r); } R operator()(int n, int r) { return C(n, r); } template <typename I> R multinomial(const vector<I>& r) { static_assert(is_integral<I>::value == true); int n = 0; for (auto& x : r) { if (x < 0) return R{0}; n += x; } R res = fac(n); for (auto& x : r) res *= finv(x); return res; } template <typename I> R operator()(const vector<I>& r) { return multinomial(r); } R P(int n, int r) { if (n < 0 || n < r || r < 0) return R(0); return fac(n) * finv(n - r); } // [x^r] 1 / (1-x)^n R H(int n, int r) { if (n < 0 || r < 0) return R(0); return r == 0 ? 1 : C(n + r - 1, r); } }; #line 2 "math/rational-fps.hpp" #line 5 "math/rational-fps.hpp" template <typename R = Rational> struct FormalPowerSeries_rational : vector<R> { using vector<R>::vector; using fps = FormalPowerSeries_rational; fps &operator+=(const fps &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i]; return *this; } fps &operator+=(const R &r) { if (this->empty()) this->resize(1); (*this)[0] += r; return *this; } fps &operator-=(const fps &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; return *this; } fps &operator-=(const R &r) { if (this->empty()) this->resize(1); (*this)[0] -= r; return *this; } fps &operator*=(const fps &r) { int n = this->size() + r.size() - 1; fps f(n); for (int i = 0; i < (int)this->size(); i++) { for (int j = 0; j < (int)r.size(); j++) { f[i + j] += (*this)[i] * r[j]; } } return *this = f; } fps &operator*=(const R &v) { for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v; return *this; } fps &operator/=(const fps &r) { if (this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; fps f(*this), g(r); g.shrink(); R coeff = g.back().inverse(); for (auto &x : g) x *= coeff; int deg = (int)f.size() - (int)g.size() + 1; int gs = g.size(); fps quo(deg); for (int i = deg - 1; i >= 0; i--) { quo[i] = f[i + gs - 1]; for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j]; } *this = quo * coeff; this->resize(n, R(0)); return *this; } fps &operator%=(const fps &r) { *this -= *this / r * r; shrink(); return *this; } fps operator+(const fps &r) const { return fps(*this) += r; } fps operator+(const R &v) const { return fps(*this) += v; } fps operator-(const fps &r) const { return fps(*this) -= r; } fps operator-(const R &v) const { return fps(*this) -= v; } fps operator*(const fps &r) const { return fps(*this) *= r; } fps operator*(const R &v) const { return fps(*this) *= v; } fps operator/(const fps &r) const { return fps(*this) /= r; } fps operator%(const fps &r) const { return fps(*this) %= r; } fps operator-() const { fps ret(this->size()); for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i]; return ret; } void shrink() { while (this->size() && this->back() == R(0)) this->pop_back(); } fps rev() const { fps ret(*this); reverse(begin(ret), end(ret)); return ret; } fps dot(fps r) const { fps ret(min(this->size(), r.size())); for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする fps pre(int sz) const { fps ret(begin(*this), begin(*this) + min((int)this->size(), sz)); if ((int)ret.size() < sz) ret.resize(sz); return ret; } fps operator>>(int sz) const { if ((int)this->size() <= sz) return {}; fps ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } fps operator<<(int sz) const { fps ret(*this); ret.insert(ret.begin(), sz, R(0)); return ret; } fps diff() const { const int n = (int)this->size(); fps ret(max(0, n - 1)); R one(1), coeff(1); for (int i = 1; i < n; i++) { ret[i - 1] = (*this)[i] * coeff; coeff += one; } return ret; } fps integral() const { const int n = (int)this->size(); fps ret(n + 1); for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (i + 1); return ret; } R eval(R x) const { R r = 0, w = 1; for (auto &v : *this) r += w * v, w *= x; return r; } fps inv(int deg = -1) const { assert((*this)[0] != R(0)); if (deg == -1) deg = (*this).size(); fps ret{R(1) / (*this)[0]}; for (int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1); } return ret.pre(deg); } fps log(int deg = -1) const { assert(!(*this).empty() && (*this)[0] == R(1)); if (deg == -1) deg = (int)this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } fps exp(int deg = -1) const { assert((*this).size() == 0 || (*this)[0] == R(0)); if (deg == -1) deg = (int)this->size(); fps ret{R(1)}; for (int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + R(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } fps pow(int64_t k, int deg = -1) const { const int n = (int)this->size(); if (deg == -1) deg = n; if (k == 0) { fps ret(deg); if (deg) ret[0] = 1; return ret; } for (int i = 0; i < n; i++) { if ((*this)[i] != R(0)) { R rev = R(1) / (*this)[i]; fps ret = (((*this * rev) >> i).log(deg) * k).exp(deg); ret *= (*this)[i].pow(k); ret = (ret << (i * k)).pre(deg); if ((int)ret.size() < deg) ret.resize(deg, R(0)); return ret; } if (__int128_t(i + 1) * k >= deg) return fps(deg, R(0)); } return fps(deg, R(0)); } }; #line 8 "verify/verify-unit-test/rational-number.test.cpp" // #line 2 "modint/montgomery-modint.hpp" template <uint32_t mod> struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); static_assert(r * mod == 1, "this code has bugs."); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint operator+() const { return mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0; while (y > 0) { t = x / y; x -= t * y, u -= t * v; tmp = x, x = y, y = tmp; tmp = u, u = v, v = tmp; } return mint{u}; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt<mod>(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; #line 2 "modulo/binomial.hpp" #line 6 "modulo/binomial.hpp" using namespace std; // コンストラクタの MAX に 「C(n, r) や fac(n) でクエリを投げる最大の n 」 // を入れると倍速くらいになる // mod を超えて前計算して 0 割りを踏むバグは対策済み template <typename T> struct Binomial { vector<T> f, g, h; Binomial(int MAX = 0) { assert(T::get_mod() != 0 && "Binomial<mint>()"); f.resize(1, T{1}); g.resize(1, T{1}); h.resize(1, T{1}); if (MAX > 0) extend(MAX + 1); } void extend(int m = -1) { int n = f.size(); if (m == -1) m = n * 2; m = min<int>(m, T::get_mod()); if (n >= m) return; f.resize(m); g.resize(m); h.resize(m); for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i); g[m - 1] = f[m - 1].inverse(); h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) { g[i] = g[i + 1] * T(i + 1); h[i] = g[i] * f[i - 1]; } } T fac(int i) { if (i < 0) return T(0); while (i >= (int)f.size()) extend(); return f[i]; } T finv(int i) { if (i < 0) return T(0); while (i >= (int)g.size()) extend(); return g[i]; } T inv(int i) { if (i < 0) return -inv(-i); while (i >= (int)h.size()) extend(); return h[i]; } T C(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } inline T operator()(int n, int r) { return C(n, r); } template <typename I> T multinomial(const vector<I>& r) { static_assert(is_integral<I>::value == true); int n = 0; for (auto& x : r) { if (x < 0) return T(0); n += x; } T res = fac(n); for (auto& x : r) res *= finv(x); return res; } template <typename I> T operator()(const vector<I>& r) { return multinomial(r); } T C_naive(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r); } // [x^r] 1 / (1-x)^n T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; #line 11 "verify/verify-unit-test/rational-number.test.cpp" using mint = LazyMontgomeryModInt<998244353>; // #line 2 "misc/rng.hpp" #line 2 "internal/internal-seed.hpp" #line 4 "internal/internal-seed.hpp" using namespace std; namespace internal { unsigned long long non_deterministic_seed() { unsigned long long m = chrono::duration_cast<chrono::nanoseconds>( chrono::high_resolution_clock::now().time_since_epoch()) .count(); m ^= 9845834732710364265uLL; m ^= m << 24, m ^= m >> 31, m ^= m << 35; return m; } unsigned long long deterministic_seed() { return 88172645463325252UL; } // 64 bit の seed 値を生成 (手元では seed 固定) // 連続で呼び出すと同じ値が何度も返ってくるので注意 // #define RANDOMIZED_SEED するとシードがランダムになる unsigned long long seed() { #if defined(NyaanLocal) && !defined(RANDOMIZED_SEED) return deterministic_seed(); #else return non_deterministic_seed(); #endif } } // namespace internal #line 4 "misc/rng.hpp" namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = internal::seed(); return _x ^= _x << 7, _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % u64(r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % u64(r - l); } // choose n numbers from [l, r) without overlapping vector<i64> randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set<i64> s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector<i64> ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } // [l, r) double rnd(double l, double r) { assert(l < r); return l + rnd() * (r - l); } template <typename T> void randshf(vector<T>& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; #line 14 "verify/verify-unit-test/rational-number.test.cpp" using namespace Nyaan; void Nyaan::solve() { { Rational a{4, 3}, b{2, 3}; assert(a + b == 2); assert(a - b == Rational(2, 3)); assert(a * b == Rational(8, 9)); assert(a / b == 2); assert(a.inverse() == Rational(3, 4)); assert(a.pow(3) == Rational(64, 27)); assert((a > b) == true); assert((a >= b) == true); assert((a < b) == false); assert((a <= b) == false); } { Binomial_rational<Rational> C; assert(C.fac(3) == 6); assert(C.finv(3) == Rational(1, 6)); assert(C(4, 2) == 6); assert(C(vi{3, 2}) == 10); } { using fps = FormalPowerSeries_rational<Rational>; { fps f{1, 2, {3, 2}}, g{{1, 4}, 5}; fps h{{5, 4}, 7, {3, 2}}; assert(f + g == h); h = fps{{3, 4}, -3, {3, 2}}; assert(f - g == h); assert(f * g % g == fps{}); assert(f * g % f == fps{}); } { fps e{1, 1, {1, 2}, {1, 6}, {1, 24}, {1, 120}}; fps f = e.pow(10); trc(f); rep(i, sz(e)) { assert(e[i] * Rational{10}.pow(i) == f[i]); } } } // mint と挙動の比較 { auto comp = [&](int i, int j, int k, int l) { rep(b, 16) { int ii = (b >> 0) % 2 ? -i : +i; int jj = (b >> 1) % 2 ? -j : +j; int kk = (b >> 2) % 2 ? -k : +k; int ll = (b >> 3) % 2 ? -l : +l; Rational x{ii, jj}, y{kk, ll}; mint X = mint{ii} / jj; mint Y = mint{kk} / ll; assert(X + Y == (x + y).to_mint(998244353)); assert(X - Y == (x - y).to_mint(998244353)); assert(X * Y == (x * y).to_mint(998244353)); if (Y != 0) { assert(X / Y == (x / y).to_mint(998244353)); } } }; rep(i, 20) rep1(j, 20) rep(k, 20) rep1(l, 20) comp(i, j, k, l); rep(t, 10000) { int lower = t % 2 ? 1 : 32000; ll i = rng(lower, 35000); ll j = rng(lower, 35000); ll k = rng(lower, 35000); ll l = rng(lower, 35000); comp(i, j, k, l); } } // binom, mint と挙動の比較 { Binomial_rational<Rational> C1; Binomial<mint> C2; reg(i, -15, 15) { assert(C2.fac(i) == C1.fac(i).to_mint(998244353)); assert(C2.finv(i) == C1.finv(i).to_mint(998244353)); assert(C2.inv(i) == C1.inv(i).to_mint(998244353)); reg(j, -15, 15) { assert(C2(i, j) == C1(i, j).to_mint(998244353)); assert(C2.P(i, j) == C1.P(i, j).to_mint(998244353)); if (i + j < 20) assert(C2.H(i, j) == C1.H(i, j).to_mint(998244353)); } } } cerr << "OK" << endl; { int s, t; cin >> s >> t; cout << s + t << "\n"; } }