#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
//
#include "../../template/template.hpp"
//
#include "../../matrix/matrix-fast.hpp"
#include "../../modint/montgomery-modint.hpp"
//
#include "../../misc/rng.hpp"
//
using namespace Nyaan;
// bitop.hpp
void verify_bitop() {
// popcnt
assert(popcnt(7) == 3);
assert(popcnt(0) == 0);
assert(popcnt(1LL << 40) == 1);
rep(loop, 100) {
u64 x = rng();
int pc = popcnt(x);
rep(i, 64) if ((x >> i) & 1) pc--;
assert(pc == 0 && "popcnt");
}
// lsb
assert(lsb(0) == 64);
assert(lsb(1) == 0);
assert(lsb(1LL << 40) == 40);
assert(lsb(100) == 2);
// ctz
assert(ctz(0) == 64);
assert(ctz(1) == 0);
assert(ctz(1LL << 40) == 40);
assert(ctz(100) == 2);
rep(loop, 100) {
u64 x = rng();
int n = lsb(x);
assert(ctz(x) == n);
while (n--) {
assert((x & 1) == 0 && "lsb");
x >>= 1;
}
assert((x & 1) == 1 && "lsb");
}
// msb
assert(msb(0) == -1);
assert(msb(1) == 0);
assert(msb(1LL << 40) == 40);
assert(msb(100) == 6);
rep(loop, 100) {
u64 x = rng();
int m = msb(x);
if (m != -1) {
assert(((x >> m) & 1) == 1 && "msb");
}
for (int i = m + 1; i < 64; i++) {
assert(((x >> i) & 1) == 0 && "msb");
}
}
// gbit, sbit
assert(gbit(5, 0) == 1);
assert(gbit(5, 1) == 0);
assert(gbit(5, 2) == 1);
assert(gbit(1LL << 40, 40) == 1);
rep(loop, 100) {
u64 x = rng();
for (int i = 0; i < 64; i++) {
u64 g = gbit(x, i);
assert(((x >> i) & 1) == g && "gbit");
sbit(x, i, 1);
assert(((x >> i) & 1) == 1u && "sbit");
sbit(x, i, 0);
assert(((x >> i) & 1) == 0u && "sbit");
sbit(x, i, g);
assert(((x >> i) & 1) == g && "sbit");
sbit(x, i, 1);
assert(((x >> i) & 1) == 1u && "sbit");
sbit(x, i, g);
assert(((x >> i) & 1) == g && "sbit");
}
}
// PW,MSK
rep(i, 63) {
assert(1LL << i == PW(i));
assert(1LL << i == MSK(i) + 1);
}
}
void verify_util() {
// P, mkp
{
pl x(3, 2);
pl y(2, 3);
assert(x + y == pl(5, 5));
assert(x - y == pl(1, -1));
assert(x * y == pl(6, 6));
x += y;
assert(x == pl(5, 5));
x -= y;
assert(x == pl(3, 2));
x *= y;
assert(x == pl(6, 6));
x *= -3;
assert(x == pl(-18, -18));
// mkp
auto p0 = mkp(1, 1);
static_assert(is_same<decltype(p0), pair<int, int>>::value);
auto p1 = mkp(1LL, double(2.0));
static_assert(is_same<decltype(p1), pair<long long, double>>::value);
assert(p0.first == 1 && p0.second == 1);
assert(p1.first == 1LL && p1.second == 2.0);
}
// P, modint
{
using mint = LazyMontgomeryModInt<998244353>;
using pm = P<mint, mint>;
pm x(3, 2);
pm y(2, 3);
assert(x + y == pm(5, 5));
assert(x - y == pm(1, -1));
assert(x * y == pm(6, 6));
x += y;
assert(x == pm(5, 5));
x -= y;
assert(x == pm(3, 2));
x *= y;
assert(x == pm(6, 6));
x *= -3;
assert(x == pm(-18, -18));
x *= mint{-3}.inverse();
assert(x == pm(6, 6));
}
// amin, amax
{
int x = 5;
amin(x, 4);
assert(x == 4);
amax(x, 5);
assert(x == 5);
}
// sz, Max, Min, Sum, mkrui, lb, ub, mkuni
{
// sz, Max, Min, Sum
vector<int> v;
for (int i = 0; i < 100; i++) {
assert(sz(v) == i);
v.push_back(randint(0, 10));
assert(Max(v) == *max_element(all(v)));
assert(Min(v) == *min_element(all(v)));
assert(Sum(v) == accumulate(all(v), 0LL));
}
// mkrui
auto rui = mkrui(v);
int buf = 0;
assert(rui[0] == 0);
rep(i, sz(v)) {
buf += v[i];
assert(rui[i + 1] == buf);
}
rui = mkrui(v, true);
buf = 0;
assert(rui.back() == 0);
repr(i, sz(v)) {
buf += v[i];
assert(rui[i] == buf);
}
// lb, ub
sort(all(v));
for (int i = 0; i < sz(v); i++) {
if (i != 0 and v[i - 1] == v[i]) continue;
int x = v[i];
assert(lb(v, x) == i);
assert(ub(v, x - 1) == i);
}
for (int x = 0; x < 10; x++) {
int l = lb(v, x);
int u = ub(v, x);
for (int i = 0; i < sz(v); i++) {
assert((l <= i) == (x <= v[i]) && "lb");
assert((u <= i) == (x < v[i]) && "ub");
}
}
// mkuni
set<int> s1, s2;
for (int i : v) s1.insert(i);
v = mkuni(v);
for (int i : v) s2.insert(i);
assert(s1 == s2);
}
// TEN
for (long long i = 0, x = 1; i <= 18; i++, x *= 10) {
assert(TEN(i) == x);
}
// mkord, mkinv(100個, 1~1000)
{
vector<int> v;
rep(loop, 100) { v.push_back(loop); }
auto ord = mkord(sz(v), [&v](int i, int j) { return v[i] < v[j]; });
rep(i, sz(ord) - 1) { assert(v[ord[i]] <= v[ord[i + 1]] && "mkord"); }
randshf(v);
auto inv = mkinv(v);
assert(inv.size() == 100 && "mkinv");
set<int> st;
each(x, v) st.insert(x);
rep(i, sz(inv)) {
if (inv[i] == -1) {
assert(st.find(i) == st.end() && "mkinv");
} else {
assert(0 <= inv[i] && inv[i] < sz(v) && "mkinv");
assert(v[inv[i]] == i && "mkinv");
}
}
}
// mkord, mkinv(100個, 1~1000)
{
vector<int> v;
rep(loop, 100) { v.push_back(randint(0, 1000)); }
auto ord = mkord(sz(v), [&v](int i, int j) { return v[i] < v[j]; });
rep(i, sz(ord) - 1) { assert(v[ord[i]] <= v[ord[i + 1]] && "mkord"); }
v = mkuni(v);
randshf(v);
auto inv = mkinv(v);
assert(sz(inv) == Max(v) + 1 && "mkinv");
set<int> st;
each(x, v) st.insert(x);
rep(i, sz(inv)) {
if (inv[i] == -1) {
assert(st.find(i) == st.end() && "mkinv");
} else {
assert(0 <= inv[i] && inv[i] < sz(v) && "mkinv");
assert(v[inv[i]] == i);
}
}
}
// mkiota
{
for (int n = 0; n < 100; n++) {
auto v = mkiota(n);
rep(i, n) assert(v[i] == i && "mkiota");
}
}
// mkrev
{
for (int n = 0; n < 100; n++) {
vi v(n);
each(x, v) x = randint(0, TEN(9));
vi w{v};
reverse(all(w));
assert(mkrev(v) == w && "mkrev");
}
for (int n = 0; n < 100; n++) {
string s;
rep(t, n) s.push_back(rng() % 26 + 'a');
string t{s};
reverse(all(t));
assert(mkrev(s) == t && "mkrev");
}
}
// nxp
{
for (int n = 0; n <= 6; n++) {
vvi v, w;
vi o = mkiota(n);
do {
v.push_back(o);
} while (nxp(o));
o = mkiota(n);
do {
w.push_back(o);
} while (next_permutation(all(o)));
assert(v == w && "nxp");
}
}
// product
{
auto v = product(vector{2LL, 3LL});
assert(sz(v) == 6);
rep(i, sz(v)) {
assert(sz(v[i]) == 2);
assert(v[i][0] == i / 3);
assert(v[i][1] == i % 3);
}
}
// Power
{
using mint = LazyMontgomeryModInt<998244353>;
{
assert(Power(3, 5) == 243);
assert(Power(10LL, 18) == TEN(18));
assert(Power(mint{2}, 30) == mint{2}.pow(30));
}
{
using Mat = Matrix<mint, 2, 2>;
Mat m;
m[0][0] = 2, m[1][1] = 1;
Mat m2 = Power(m, 10, Mat::I());
assert(m2[0][0] == 1024);
assert(m2[0][1] == 0);
assert(m2[1][0] == 0);
assert(m2[1][1] == 1);
}
for (ll x = 1; x <= 100; x++) {
i128 y = 1;
for (ll e = 0; e <= 64; e++) {
ll z1 = Power<ll>(x, e, 1);
ll z2 = Power<ll>(x, e, 1, [](ll& a) { a %= 998244353; });
mint z3 = Power<mint>(x, e, 1);
assert(z1 == y);
assert(z2 == y % 998244353);
assert(z3.get() == z2);
y *= x;
if (y >= 8 * TEN(18)) break;
}
}
}
// Rev
{
vector a{1, 2, 3};
vector a2{3, 2, 1};
assert(Rev(a) == a2);
string b = "abc";
string b2 = "cba"s;
assert(Rev(b) == b2);
vector c{vector{1}, vector{1, 2}};
vector c2{vector{1, 2}, vector{1}};
assert(Rev(c) == c2);
}
// Transpose, Rotate
{
vector b{"abc"s, "def"s};
vector b2{"ad"s, "be"s, "cf"s};
vector b3{"cf"s, "be"s, "ad"s};
vector b4{"da"s, "eb"s, "fc"s};
assert(b2 == Transpose(b));
assert(b3 == Rotate(b));
assert(b4 == Rotate(b, 0));
}
}
void Nyaan::solve() {
verify_bitop();
verify_util();
cerr << "OK" << endl;
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
#line 1 "verify/verify-unit-test/template.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(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 = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // 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 __builtin_popcountll(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(std::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/template.test.cpp"
//
#line 2 "matrix/matrix-fast.hpp"
template <typename T, int H, int W>
struct Matrix {
using Array = array<array<T, W>, H>;
Array A;
Matrix() : A() {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) (*this)[i][j] = T();
}
int height() const { return H; }
int width() const { return W; }
inline const array<T, W> &operator[](int k) const { return A[k]; }
inline array<T, W> &operator[](int k) { return A[k]; }
static Matrix I() {
assert(H == W);
Matrix mat;
for (int i = 0; i < H; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++) A[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
assert(H == W);
Matrix C;
for (int i = 0; i < H; i++)
for (int k = 0; k < H; k++)
for (int j = 0; j < H; j++) C[i][j] += A[i][k] * B[k][j];
A.swap(C.A);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I();
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
for (int i = 0; i < H; i++)
for (int j = 0; j < W; j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
friend ostream &operator<<(ostream &os,const Matrix &p) {
for (int i = 0; i < H; i++) {
os << "[";
for (int j = 0; j < W; j++) {
os << p[i][j] << (j + 1 == W ? "]\n" : ",");
}
}
return (os);
}
T determinant(int n = -1) {
if (n == -1) n = H;
Matrix B(*this);
T ret = 1;
for (int i = 0; i < n; i++) {
int idx = -1;
for (int j = i; j < n; j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < n; j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < n; j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < n; k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
/**
* @brief 行列ライブラリ(std::array版)
*/
#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 7 "verify/verify-unit-test/template.test.cpp"
//
#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);
sort(begin(ret), end(ret));
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 9 "verify/verify-unit-test/template.test.cpp"
//
using namespace Nyaan;
// bitop.hpp
void verify_bitop() {
// popcnt
assert(popcnt(7) == 3);
assert(popcnt(0) == 0);
assert(popcnt(1LL << 40) == 1);
rep(loop, 100) {
u64 x = rng();
int pc = popcnt(x);
rep(i, 64) if ((x >> i) & 1) pc--;
assert(pc == 0 && "popcnt");
}
// lsb
assert(lsb(0) == 64);
assert(lsb(1) == 0);
assert(lsb(1LL << 40) == 40);
assert(lsb(100) == 2);
// ctz
assert(ctz(0) == 64);
assert(ctz(1) == 0);
assert(ctz(1LL << 40) == 40);
assert(ctz(100) == 2);
rep(loop, 100) {
u64 x = rng();
int n = lsb(x);
assert(ctz(x) == n);
while (n--) {
assert((x & 1) == 0 && "lsb");
x >>= 1;
}
assert((x & 1) == 1 && "lsb");
}
// msb
assert(msb(0) == -1);
assert(msb(1) == 0);
assert(msb(1LL << 40) == 40);
assert(msb(100) == 6);
rep(loop, 100) {
u64 x = rng();
int m = msb(x);
if (m != -1) {
assert(((x >> m) & 1) == 1 && "msb");
}
for (int i = m + 1; i < 64; i++) {
assert(((x >> i) & 1) == 0 && "msb");
}
}
// gbit, sbit
assert(gbit(5, 0) == 1);
assert(gbit(5, 1) == 0);
assert(gbit(5, 2) == 1);
assert(gbit(1LL << 40, 40) == 1);
rep(loop, 100) {
u64 x = rng();
for (int i = 0; i < 64; i++) {
u64 g = gbit(x, i);
assert(((x >> i) & 1) == g && "gbit");
sbit(x, i, 1);
assert(((x >> i) & 1) == 1u && "sbit");
sbit(x, i, 0);
assert(((x >> i) & 1) == 0u && "sbit");
sbit(x, i, g);
assert(((x >> i) & 1) == g && "sbit");
sbit(x, i, 1);
assert(((x >> i) & 1) == 1u && "sbit");
sbit(x, i, g);
assert(((x >> i) & 1) == g && "sbit");
}
}
// PW,MSK
rep(i, 63) {
assert(1LL << i == PW(i));
assert(1LL << i == MSK(i) + 1);
}
}
void verify_util() {
// P, mkp
{
pl x(3, 2);
pl y(2, 3);
assert(x + y == pl(5, 5));
assert(x - y == pl(1, -1));
assert(x * y == pl(6, 6));
x += y;
assert(x == pl(5, 5));
x -= y;
assert(x == pl(3, 2));
x *= y;
assert(x == pl(6, 6));
x *= -3;
assert(x == pl(-18, -18));
// mkp
auto p0 = mkp(1, 1);
static_assert(is_same<decltype(p0), pair<int, int>>::value);
auto p1 = mkp(1LL, double(2.0));
static_assert(is_same<decltype(p1), pair<long long, double>>::value);
assert(p0.first == 1 && p0.second == 1);
assert(p1.first == 1LL && p1.second == 2.0);
}
// P, modint
{
using mint = LazyMontgomeryModInt<998244353>;
using pm = P<mint, mint>;
pm x(3, 2);
pm y(2, 3);
assert(x + y == pm(5, 5));
assert(x - y == pm(1, -1));
assert(x * y == pm(6, 6));
x += y;
assert(x == pm(5, 5));
x -= y;
assert(x == pm(3, 2));
x *= y;
assert(x == pm(6, 6));
x *= -3;
assert(x == pm(-18, -18));
x *= mint{-3}.inverse();
assert(x == pm(6, 6));
}
// amin, amax
{
int x = 5;
amin(x, 4);
assert(x == 4);
amax(x, 5);
assert(x == 5);
}
// sz, Max, Min, Sum, mkrui, lb, ub, mkuni
{
// sz, Max, Min, Sum
vector<int> v;
for (int i = 0; i < 100; i++) {
assert(sz(v) == i);
v.push_back(randint(0, 10));
assert(Max(v) == *max_element(all(v)));
assert(Min(v) == *min_element(all(v)));
assert(Sum(v) == accumulate(all(v), 0LL));
}
// mkrui
auto rui = mkrui(v);
int buf = 0;
assert(rui[0] == 0);
rep(i, sz(v)) {
buf += v[i];
assert(rui[i + 1] == buf);
}
rui = mkrui(v, true);
buf = 0;
assert(rui.back() == 0);
repr(i, sz(v)) {
buf += v[i];
assert(rui[i] == buf);
}
// lb, ub
sort(all(v));
for (int i = 0; i < sz(v); i++) {
if (i != 0 and v[i - 1] == v[i]) continue;
int x = v[i];
assert(lb(v, x) == i);
assert(ub(v, x - 1) == i);
}
for (int x = 0; x < 10; x++) {
int l = lb(v, x);
int u = ub(v, x);
for (int i = 0; i < sz(v); i++) {
assert((l <= i) == (x <= v[i]) && "lb");
assert((u <= i) == (x < v[i]) && "ub");
}
}
// mkuni
set<int> s1, s2;
for (int i : v) s1.insert(i);
v = mkuni(v);
for (int i : v) s2.insert(i);
assert(s1 == s2);
}
// TEN
for (long long i = 0, x = 1; i <= 18; i++, x *= 10) {
assert(TEN(i) == x);
}
// mkord, mkinv(100個, 1~1000)
{
vector<int> v;
rep(loop, 100) { v.push_back(loop); }
auto ord = mkord(sz(v), [&v](int i, int j) { return v[i] < v[j]; });
rep(i, sz(ord) - 1) { assert(v[ord[i]] <= v[ord[i + 1]] && "mkord"); }
randshf(v);
auto inv = mkinv(v);
assert(inv.size() == 100 && "mkinv");
set<int> st;
each(x, v) st.insert(x);
rep(i, sz(inv)) {
if (inv[i] == -1) {
assert(st.find(i) == st.end() && "mkinv");
} else {
assert(0 <= inv[i] && inv[i] < sz(v) && "mkinv");
assert(v[inv[i]] == i && "mkinv");
}
}
}
// mkord, mkinv(100個, 1~1000)
{
vector<int> v;
rep(loop, 100) { v.push_back(randint(0, 1000)); }
auto ord = mkord(sz(v), [&v](int i, int j) { return v[i] < v[j]; });
rep(i, sz(ord) - 1) { assert(v[ord[i]] <= v[ord[i + 1]] && "mkord"); }
v = mkuni(v);
randshf(v);
auto inv = mkinv(v);
assert(sz(inv) == Max(v) + 1 && "mkinv");
set<int> st;
each(x, v) st.insert(x);
rep(i, sz(inv)) {
if (inv[i] == -1) {
assert(st.find(i) == st.end() && "mkinv");
} else {
assert(0 <= inv[i] && inv[i] < sz(v) && "mkinv");
assert(v[inv[i]] == i);
}
}
}
// mkiota
{
for (int n = 0; n < 100; n++) {
auto v = mkiota(n);
rep(i, n) assert(v[i] == i && "mkiota");
}
}
// mkrev
{
for (int n = 0; n < 100; n++) {
vi v(n);
each(x, v) x = randint(0, TEN(9));
vi w{v};
reverse(all(w));
assert(mkrev(v) == w && "mkrev");
}
for (int n = 0; n < 100; n++) {
string s;
rep(t, n) s.push_back(rng() % 26 + 'a');
string t{s};
reverse(all(t));
assert(mkrev(s) == t && "mkrev");
}
}
// nxp
{
for (int n = 0; n <= 6; n++) {
vvi v, w;
vi o = mkiota(n);
do {
v.push_back(o);
} while (nxp(o));
o = mkiota(n);
do {
w.push_back(o);
} while (next_permutation(all(o)));
assert(v == w && "nxp");
}
}
// product
{
auto v = product(vector{2LL, 3LL});
assert(sz(v) == 6);
rep(i, sz(v)) {
assert(sz(v[i]) == 2);
assert(v[i][0] == i / 3);
assert(v[i][1] == i % 3);
}
}
// Power
{
using mint = LazyMontgomeryModInt<998244353>;
{
assert(Power(3, 5) == 243);
assert(Power(10LL, 18) == TEN(18));
assert(Power(mint{2}, 30) == mint{2}.pow(30));
}
{
using Mat = Matrix<mint, 2, 2>;
Mat m;
m[0][0] = 2, m[1][1] = 1;
Mat m2 = Power(m, 10, Mat::I());
assert(m2[0][0] == 1024);
assert(m2[0][1] == 0);
assert(m2[1][0] == 0);
assert(m2[1][1] == 1);
}
for (ll x = 1; x <= 100; x++) {
i128 y = 1;
for (ll e = 0; e <= 64; e++) {
ll z1 = Power<ll>(x, e, 1);
ll z2 = Power<ll>(x, e, 1, [](ll& a) { a %= 998244353; });
mint z3 = Power<mint>(x, e, 1);
assert(z1 == y);
assert(z2 == y % 998244353);
assert(z3.get() == z2);
y *= x;
if (y >= 8 * TEN(18)) break;
}
}
}
// Rev
{
vector a{1, 2, 3};
vector a2{3, 2, 1};
assert(Rev(a) == a2);
string b = "abc";
string b2 = "cba"s;
assert(Rev(b) == b2);
vector c{vector{1}, vector{1, 2}};
vector c2{vector{1, 2}, vector{1}};
assert(Rev(c) == c2);
}
// Transpose, Rotate
{
vector b{"abc"s, "def"s};
vector b2{"ad"s, "be"s, "cf"s};
vector b3{"cf"s, "be"s, "ad"s};
vector b4{"da"s, "eb"s, "fc"s};
assert(b2 == Transpose(b));
assert(b3 == Rotate(b));
assert(b4 == Rotate(b, 0));
}
}
void Nyaan::solve() {
verify_bitop();
verify_util();
cerr << "OK" << endl;
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
verify/verify-unit-test/template.test.cpp