結果

問題 No.1100 Boxes
ユーザー cn_449
提出日時 2020-06-26 23:08:11
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 87 ms / 2,000 ms
コード長 6,242 bytes
コンパイル時間 1,339 ms
コンパイル使用メモリ 124,380 KB
実行使用メモリ 16,360 KB
最終ジャッジ日時 2024-07-04 23:34:32
合計ジャッジ時間 3,600 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 36
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <iomanip>
#include <utility>
#include <tuple>
#include <functional>
#include <bitset>
#include <cassert>
#include <complex>
#include <stdio.h>
#include <time.h>
#include <numeric>
#include <random>
#include <unordered_map>
#include <unordered_set>
#define all(a) a.begin(),a.end()
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define pb push_back
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll, ll> P;
typedef complex<ld> com;
constexpr int inf = 1000000010;
constexpr ll INF = 1000000000000000010;
constexpr ld eps = 1e-12;
constexpr ld pi = 3.141592653589793238;
template<class T, class U> inline bool chmax(T &a, const U &b) { if (a < b) { a = b; return true; } return false; }
template<class T, class U> inline bool chmin(T &a, const U &b) { if (a > b) { a = b; return true; } return false; }
constexpr ll mod = 998244353;
constexpr ll modsize = 200000;
vector<ll> fac(modsize);
vector<ll> inv(modsize);
vector<ll> facinv(modsize);
void modcalc() {
if (modsize == 0) abort();
fac[0] = 1; fac[1] = 1; inv[1] = 1;
facinv[0] = 1; facinv[1] = 1;
for (ll i = 2; i < modsize; i++) {
fac[i] = fac[i - 1] * i % mod;
inv[i] = mod - inv[mod % i] * (mod / i) % mod;
facinv[i] = facinv[i - 1] * inv[i] % mod;
}
}
ll modinv(ll a) {
if (a == 0) abort();
ll b = mod, u = 1, v = 0;
while (b) {
ll t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
ll modpow(ll a, ll b) {
ll ans = 1;
a %= mod;
while (b) {
if (b & 1) ans = ans * a % mod;
a = a * a % mod;
b >>= 1;
}
return ans;
}
ll modcomb(ll n, ll k) {
if (n < 0 || k < 0 || n < k) return 0;
return fac[n] * facinv[k] % mod * facinv[n - k] % mod;
}
ll modperm(ll n, ll k) {
if (n < 0 || k < 0 || n < k) return 0;
return fac[n] * facinv[n - k] % mod;
}
ll modhom(ll n, ll k) {
if (n < 0 || k < 0 || n == 0 && k > 0) return 0;
if (n == 0 && k == 0) return 1;
return fac[n + k - 1] * facinv[k] % mod * facinv[n - 1] % mod;
}
template<int mod, int root = 3> class NumberTheoreticTransform {
inline static constexpr long long gcd(long long a, long long b) {
return (b ? gcd(b, a % b) : a);
}
inline static long long ext_gcd(long long a, long long b, long long &x, long long &y) {
long long res;
if (b == 0) res = a, x = 1, y = 0;
else res = ext_gcd(b, a%b, y, x), y -= a / b * x;
return res;
}
inline static long long inv_mod(long long a, long long b) {
long long x, y;
ext_gcd(a, b, x, y);
return (x%b + b) % b;
}
inline static long long pow_mod(long long x, long long n, long long m) {
long long res = 1;
for (; n > 0; n >>= 1, (x *= x) %= m) if (n & 1) (res *= x) %= m;
return res;
}
inline static long long garner(vector<long long> b, vector<long long> m, long long d) {
int N = b.size();
vector<long long> coe(N + 1, 1), val(N + 1, 0);
long long g, gl, gr, sum = accumulate(b.begin(), b.end(), 0LL);
for (int l = 0; l < N; ++l) {
for (int r = l + 1; r < N; ++r) {
g = gcd(m[l], m[r]);
if (sum && (b[l] - b[r]) % g != 0) return -1;
m[l] /= g, m[r] /= g;
gl = gcd(m[l], g), gr = g / gl;
do {
g = gcd(gl, gr);
gl *= g, gr /= g;
} while (g != 1);
m[l] *= gl, m[r] *= gr;
b[l] %= m[l], b[r] %= m[r];
}
}
if (!sum) {
long long lcm = 1;
for (auto& e : m) (lcm *= e) %= d;
return lcm;
}
m.push_back(d);
for (int i = 0; i < N; ++i) {
long long t = (b[i] - val[i]) * inv_mod(coe[i], m[i]);
((t %= m[i]) += m[i]) %= m[i];
for (int j = i + 1; j <= N; ++j) {
(val[j] += t * coe[j]) %= m[j];
(coe[j] *= m[i]) %= m[j];
}
}
return val.back();
}
inline static void ntt(vector<long long>& f, int sgn = 1) {
int N = f.size();
int h = pow_mod(root, (mod - 1) / N, mod);
if (sgn == -1) h = inv_mod(h, mod);
for (int i = 0, j = 1; j < N - 1; ++j) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (j < i) swap(f[i], f[j]);
}
for (int i = 1, j = 2; i < N; i *= 2, j *= 2) {
long long w = 1, base = pow_mod(h, N / j, mod);
for (int k = 0; k < i; ++k, (w *= base) %= mod) {
for (int l = k; l < N; l += j) {
long long u = f[l];
long long d = f[l + i] * w % mod;
f[l] = u + d;
if (f[l] >= mod) f[l] -= mod;
f[l + i] = u - d;
if (f[l + i] < 0) f[l + i] += mod;
}
}
}
for (auto& x : f) if (x < 0) x += mod;
}
public:
inline static vector<long long> convolution(vector<long long> g, vector<long long> h) {
int N; for (N = 1; N < g.size() + h.size(); N *= 2);
vector<long long> f(N);
g.resize(N); h.resize(N);
ntt(g); ntt(h);
for (int i = 0; i < N; ++i) (f[i] = g[i] * h[i]) %= mod;
ntt(f, -1);
long long inv = inv_mod(N, mod);
for (auto& x : f) x = x * inv % mod;
return f;
}
inline static vector<long long> convolution_arbitrarymod(vector<long long> g, vector<long long> h) {
for (auto& a : g) a %= mod;
for (auto& a : h) a %= mod;
const int mod1 = 167772161;
const int mod2 = 469762049;
const int mod3 = 1224736769;
auto x = NumberTheoreticTransform<mod1>::convolution(g, h);
auto y = NumberTheoreticTransform<mod2>::convolution(g, h);
auto z = NumberTheoreticTransform<mod3>::convolution(g, h);
vector<long long> res(x.size()), b(3), m(3);
for (int i = 0; i < x.size(); ++i) {
m[0] = mod1, b[0] = x[i];
m[1] = mod2, b[1] = y[i];
m[2] = mod3, b[2] = z[i];
res[i] = garner(b, m, mod);
}
return res;
}
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(20);
modcalc();
ll n, k;
cin >> n >> k;
vector<ll> a(k + 1), b(k + 1);
rep(i, k + 1) {
if (i & 1) b[i] = facinv[i];
if ((k & 1) != (i & 1)) a[i] = modpow(i, n) * facinv[i] % mod;
else {
a[i] = mod - modpow(i, n) * facinv[i] % mod;
if (a[i] >= mod) a[i] -= mod;
}
}
vector<ll> c = NumberTheoreticTransform<998244353>::convolution(a, b);
ll ans = 0;
rep(i, k + 1) ans += c[i] * facinv[k - i] % mod;
ans %= mod;
cout << ans * fac[k] % mod << '\n';
}
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