#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" // #include "../../template/template.hpp" // #include "../../math/nimber.hpp" #include "../../misc/rng.hpp" #include "../../modint/montgomery-modint.hpp" #include "../../ntt/karatsuba.hpp" using namespace Nyaan; template <typename T> vector<T> naive(vector<T>& a, vector<T>& b) { vector<T> c(a.size() + b.size() - 1); rep(i, sz(a)) rep(j, sz(b)) c[i + j] += a[i] * b[j]; return c; } template <typename T> void test() { int mx = 500; rep(_, 100) { int s = randint(1, mx); int t = randint(1, mx); vector<T> a(s), b(t); each(x, a) x = rng(); each(x, b) x = rng(); auto c = karatsuba(a, b); auto d = naive(a, b); assert(c == d); } cerr << "OK" << endl; } void Nyaan::solve() { test<LazyMontgomeryModInt<998244353>>(); test<Nimber64>(); test<Nimber32>(); test<Nimber16>(); test<uint32_t>(); test<uint64_t>(); int a, b; cin >> a >> b; cout << a + b << endl; }
#line 1 "verify/verify-unit-test/karatsuba.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/karatsuba.test.cpp" // #line 2 "math/nimber.hpp" #line 2 "math/garner.hpp" // input : a, M (0 < a < M) // output : pair(g, x) s.t. g = gcd(a, M), xa = g (mod M), 0 <= x < b/g template <typename uint> pair<uint, uint> gcd_inv(uint a, uint M) { assert(M != 0 && 0 < a); a %= M; uint b = M, s = 1, t = 0; while (true) { if (a == 0) return {b, t + M}; t -= b / a * s; b %= a; if (b == 0) return {a, s}; s -= a / b * t; a %= b; } } // 入力 : 0 <= rem[i] < mod[i], 1 <= mod[i] // 存在するとき : return {rem, mod} // 存在しないとき : return {0, 0} template <typename T, typename U> pair<unsigned long long, unsigned long long> garner(const vector<T>& rem, const vector<U>& mod) { assert(rem.size() == mod.size()); using u64 = unsigned long long; u64 r0 = 0, m0 = 1; for (int i = 0; i < (int)rem.size(); i++) { assert(1 <= mod[i]); assert(0 <= rem[i] && rem[i] < mod[i]); u64 m1 = mod[i], r1 = rem[i] % m1; if (m0 < m1) swap(r0, r1), swap(m0, m1); if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } u64 g, im; tie(g, im) = gcd_inv(m0, m1); u64 y = r0 < r1 ? r1 - r0 : r0 - r1; if (y % g != 0) return {0, 0}; u64 u1 = m1 / g; y = y / g % u1; if (r0 > r1 && y != 0) y = u1 - y; u64 x = y * im % u1; r0 += x * m0; m0 *= u1; } return {r0, m0}; } /** * @brief Garner's algorithm */ #line 4 "math/nimber.hpp" namespace NimberImpl { using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; struct calc8 { u16 dp[1 << 8][1 << 8]; constexpr calc8() : dp() { dp[0][0] = dp[0][1] = dp[1][0] = 0; dp[1][1] = 1; for (int e = 1; e <= 3; e++) { int p = 1 << e, q = p >> 1; u16 ep = 1u << p, eq = 1u << q; for (u16 i = 0; i < ep; i++) { for (u16 j = i; j < ep; j++) { if (i < eq && j < eq) continue; if (min(i, j) <= 1u) { dp[i][j] = dp[j][i] = i * j; continue; } u16 iu = i >> q, il = i & (eq - 1); u16 ju = j >> q, jl = j & (eq - 1); u16 u = dp[iu][ju], l = dp[il][jl]; u16 ul = dp[iu ^ il][ju ^ jl]; u16 uq = dp[u][eq >> 1]; dp[i][j] = ((ul ^ l) << q) ^ uq ^ l; dp[j][i] = dp[i][j]; } } } } } constexpr c8; struct calc16 { static constexpr u16 proot = 10279; static constexpr u32 ppoly = 92191; static constexpr int order = 65535; u16 base[16], exp[(1 << 18) + 100]; int log[1 << 16]; private: constexpr u16 d(u32 x) { return (x << 1) ^ (x < 32768u ? 0 : ppoly); } constexpr u16 naive(u16 i, u16 j) { if (min(i, j) <= 1u) return i * j; u16 q = 8, eq = 1u << 8; u16 iu = i >> q, il = i & (eq - 1); u16 ju = j >> q, jl = j & (eq - 1); u16 u = c8.dp[iu][ju]; u16 l = c8.dp[il][jl]; u16 ul = c8.dp[iu ^ il][ju ^ jl]; u16 uq = c8.dp[u][eq >> 1]; return ((ul ^ l) << q) ^ uq ^ l; } public: constexpr calc16() : base(), exp(), log() { base[0] = 1; for (int i = 1; i < 16; i++) base[i] = naive(base[i - 1], proot); exp[0] = 1; for (int i = 1; i < order; i++) exp[i] = d(exp[i - 1]); u16* pre = exp + order + 1; pre[0] = 0; for (int b = 0; b < 16; b++) { int is = 1 << b, ie = is << 1; for (int i = is; i < ie; i++) pre[i] = pre[i - is] ^ base[b]; } for (int i = 0; i < order; i++) exp[i] = pre[exp[i]], log[exp[i]] = i; int ie = 2 * order + 30; for (int i = order; i < ie; i++) exp[i] = exp[i - order]; for (unsigned int i = ie; i < sizeof(exp) / sizeof(u16); i++) exp[i] = 0; log[0] = ie + 1; } constexpr u16 prod(u16 i, u16 j) const { return exp[log[i] + log[j]]; } // exp[3] = 2^{15} = 32768 constexpr u16 Hprod(u16 i, u16 j) const { return exp[log[i] + log[j] + 3]; } constexpr u16 H(u16 i) const { return exp[log[i] + 3]; } constexpr u16 H2(u16 i) const { return exp[log[i] + 6]; } } constexpr c16; u16 product16(u16 i, u16 j) { return c16.prod(i, j); } constexpr u32 product32(u32 i, u32 j) { u16 iu = i >> 16, il = i & 65535; u16 ju = j >> 16, jl = j & 65535; u16 l = c16.prod(il, jl); u16 ul = c16.prod(iu ^ il, ju ^ jl); u16 uq = c16.Hprod(iu, ju); return (u32(ul ^ l) << 16) ^ uq ^ l; } // (+ : xor, x : nim product, * : integer product) // i x j // = (iu x ju + il x ju + iu x ji) * 2^{16} // + (iu x ju x 2^{15}) + il x jl // (assign ju = 2^{15}, jl = 0) // = ((iu + il) x 2^{15}) * 2^{16} + (iu x 2^{15} x 2^{15}) constexpr u32 H(u32 i) { u16 iu = i >> 16; u16 il = i & 65535; return (u32(c16.H(iu ^ il)) << 16) ^ c16.H2(iu); } constexpr u64 product64(u64 i, u64 j) { u32 iu = i >> 32, il = i & u32(-1); u32 ju = j >> 32, jl = j & u32(-1); u32 l = product32(il, jl); u32 ul = product32(iu ^ il, ju ^ jl); u32 uq = H(product32(iu, ju)); return (u64(ul ^ l) << 32) ^ uq ^ l; } } // namespace NimberImpl template <typename uint, uint (*prod)(uint, uint)> struct NimberBase { using N = NimberBase; uint x; NimberBase() : x(0) {} NimberBase(uint _x) : x(_x) {} static N id0() { return {}; } static N id1() { return {1}; } N& operator+=(const N& p) { x ^= p.x; return *this; } N& operator-=(const N& p) { x ^= p.x; return *this; } N& operator*=(const N& p) { x = prod(x, p.x); return *this; } N operator+(const N& p) const { return x ^ p.x; } N operator-(const N& p) const { return x ^ p.x; } N operator*(const N& p) const { return prod(x, p.x); } bool operator==(const N& p) const { return x == p.x; } bool operator!=(const N& p) const { return x != p.x; } N pow(uint64_t n) const { N a = *this, r = 1; for (; n; a *= a, n >>= 1) if (n & 1) r *= a; return r; } friend ostream& operator<<(ostream& os, const N& p) { return os << p.x; } // calculate log_a (b) uint discrete_logarithm(N y) const { assert(x != 0 && y != 0); vector<uint> rem, mod; for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) { if (uint(-1) % p) continue; uint q = uint(-1) / p; uint STEP = 1; while (4 * STEP * STEP < p) STEP *= 2; // a^m = z を満たす 1 以上の整数 m を返す auto inside = [&](N a, N z) -> uint { unordered_map<uint, int> mp; N big = 1, now = 1; // x^m for (int i = 0; i < int(STEP); i++) { mp[z.x] = i, z *= a, big *= a; } for (int step = 0; step < int(p + 10); step += STEP) { now *= big; if (mp.find(now.x) != mp.end()) return (step + STEP) - mp[now.x]; } return uint(-1); }; N xq = (*this).pow(q), yq = y.pow(q); if (xq == 1 and yq == 1) continue; if (xq == 1 and yq != 1) return uint(-1); uint res = inside(xq, yq); if (res == uint(-1)) return uint(-1); rem.push_back(res % p); mod.push_back(p); } return garner(rem, mod).first; } uint is_primitive_root() const { if (x == 0) return false; for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) { if (uint(-1) % p != 0) continue; if ((*this).pow(uint(-1) / p) == 1) return false; } return true; } }; using Nimber16 = NimberBase<uint16_t, NimberImpl::product16>; using Nimber32 = NimberBase<uint32_t, NimberImpl::product32>; using Nimber64 = NimberBase<uint64_t, NimberImpl::product64>; using Nimber = Nimber64; /** * @brief Nim Product * @docs docs/math/nimber.md */ #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 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 "ntt/karatsuba.hpp" namespace KaratsubaImpl { template <typename T> vector<T> naive(const vector<T>& a, const vector<T>& b) { if (a.empty() and b.empty()) return {}; if (a.size() < b.size()) return naive(b, a); int s = a.size(), t = b.size(); vector<T> c(s + t - 1); for (int i = 0; i < s; i++) { for (int j = 0; j < t; j++) c[i + j] += a[i] * b[j]; } return c; } template <typename T> void add(vector<T>& a, const vector<T>& b) { if (a.size() < b.size()) a.resize(b.size()); for (int i = 0; i < (int)b.size(); i++) a[i] += b[i]; } template <typename T> void sub(vector<T>& a, const vector<T>& b) { if (a.size() < b.size()) a.resize(b.size()); for (int i = 0; i < (int)b.size(); i++) a[i] -= b[i]; } template <typename T> vector<T> karatsuba(const vector<T>& a, const vector<T>& b) { if (a.empty() and b.empty()) return {}; if (a.size() < b.size()) return karatsuba(b, a); if (a.size() < 32) return naive(a, b); int d = a.size() / 2; vector<T> al{begin(a), begin(a) + d}, au{begin(a) + d, end(a)}; if ((int)b.size() < d + 10) { auto cl = karatsuba(al, b); auto cu = karatsuba(au, b); vector<T> c(a.size() + b.size() - 1); for (int i = 0; i < (int)cl.size(); i++) c[i] = cl[i]; for (int i = 0; i < (int)cu.size(); i++) c[i + d] += cu[i]; return c; } vector<T> bl{begin(b), begin(b) + d}, bu{begin(b) + d, end(b)}; vector<T> alu{al}, blu{bl}; add(alu, au), add(blu, bu); auto cll = karatsuba(al, bl); auto cuu = karatsuba(au, bu); auto clu = karatsuba(alu, blu); sub(clu, cll), sub(clu, cuu); vector<T> c(d); copy(begin(clu), end(clu), back_inserter(c)); c.resize(a.size() + b.size() - 1); add(c, cll); for (int i = 0; i < (int)cuu.size(); i++) c[i + 2 * d] += cuu[i]; c.resize(a.size() + b.size() - 1); return c; } } // namespace KaratsubaImpl using KaratsubaImpl::karatsuba; #line 9 "verify/verify-unit-test/karatsuba.test.cpp" using namespace Nyaan; template <typename T> vector<T> naive(vector<T>& a, vector<T>& b) { vector<T> c(a.size() + b.size() - 1); rep(i, sz(a)) rep(j, sz(b)) c[i + j] += a[i] * b[j]; return c; } template <typename T> void test() { int mx = 500; rep(_, 100) { int s = randint(1, mx); int t = randint(1, mx); vector<T> a(s), b(t); each(x, a) x = rng(); each(x, b) x = rng(); auto c = karatsuba(a, b); auto d = naive(a, b); assert(c == d); } cerr << "OK" << endl; } void Nyaan::solve() { test<LazyMontgomeryModInt<998244353>>(); test<Nimber64>(); test<Nimber32>(); test<Nimber16>(); test<uint32_t>(); test<uint64_t>(); int a, b; cin >> a >> b; cout << a + b << endl; }