結果
問題 | No.1100 Boxes |
ユーザー |
![]() |
提出日時 | 2020-06-26 22:34:34 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 91 ms / 2,000 ms |
コード長 | 13,381 bytes |
コンパイル時間 | 3,058 ms |
コンパイル使用メモリ | 228,316 KB |
最終ジャッジ日時 | 2025-01-11 11:52:17 |
ジャッジサーバーID (参考情報) |
judge3 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 36 |
ソースコード
#include <bits/stdc++.h>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); returnvec; }template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; returnos; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os;}template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}";return os; }template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << "(" << pa.first << "," << pa.second << ")";return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first <<"=>" << v.second << ","; os << "}"; return os; }#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;template <int mod>struct ModInt{using lint = long long;static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&](){std::set<int> fac;int v = mod - 1;for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}int val;constexpr ModInt() : val(0) {}constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }constexpr ModInt(lint v) { _setval(v % mod + mod); }explicit operator bool() const { return val != 0; }constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }constexpr bool operator==(const ModInt &x) const { return val == x.val; }constexpr bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }constexpr lint power(lint n) const {lint ans = 1, tmp = this->val;while (n) {if (n & 1) ans = ans * tmp % mod;tmp = tmp * tmp % mod;n /= 2;}return ans;}constexpr lint inv() const { return this->power(mod - 2); }constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }inline ModInt fac() const {static std::vector<ModInt> facs;int l0 = facs.size();if (l0 > this->val) return facs[this->val];facs.resize(this->val + 1);for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));return facs[this->val];}ModInt doublefac() const {lint k = (this->val + 1) / 2;if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();else return ModInt(k).fac() * ModInt(2).power(k);}ModInt nCr(const ModInt &r) const {if (this->val < r.val) return ModInt(0);return this->fac() / ((*this - r).fac() * r.fac());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (power((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.power((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.power(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, mod - x.val));}};constexpr lint MOD = 998244353;using mint = ModInt<MOD>;// Integer convolution for arbitrary mod// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.// input: a (size: n), b (size: m)// return: vector (size: n + m - 1)template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false);constexpr int nttprimes[3] = {998244353, 167772161, 469762049};// Integer FFT (Fast Fourier Transform) for ModInt class// (Also known as Number Theoretic Transform, NTT)// is_inverse: inverse transform// ** Input size must be 2^n **template <typename MODINT>void ntt(std::vector<MODINT> &a, bool is_inverse = false){int n = a.size();if (n == 1) return;static const int mod = MODINT::get_mod();static const MODINT root = MODINT::get_primitive_root();assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);static std::vector<MODINT> w{1}, iw{1};for (int m = w.size(); m < n / 2; m *= 2){MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw;w.resize(m * 2), iw.resize(m * 2);for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;}if (!is_inverse) {for (int m = n; m >>= 1;) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {#ifdef __clang__a[i + m] *= w[k];std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);#elseMODINT x = a[i], y = a[i + m] * w[k];a[i] = x + y, a[i + m] = x - y;#endif}}}}else {for (int m = 1; m < n; m *= 2) {for (int s = 0, k = 0; s < n; s += 2 * m, k++) {for (int i = s; i < s + m; i++) {#ifdef __clang__std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);a[i + m] *= iw[k];#elseMODINT x = a[i], y = a[i + m];a[i] = x + y, a[i + m] = (x - y) * iw[k];#endif}}}int n_inv = MODINT(n).inv();for (auto &v : a) v *= n_inv;}}template <int MOD>std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {int sz = a.size();assert(a.size() == b.size() and __builtin_popcount(sz) == 1);std::vector<ModInt<MOD>> ap(sz), bp(sz);for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];if (a == b) {ntt(ap, false);bp = ap;}else {ntt(ap, false);ntt(bp, false);}for (int i = 0; i < sz; i++) ap[i] *= bp[i];ntt(ap, true);return ap;}long long extgcd_ntt_(long long a, long long b, long long &x, long long &y){long long d = a;if (b != 0) d = extgcd_ntt_(b, a % b, y, x), y -= (a / b) * x;else x = 1, y = 0;return d;}long long modinv_ntt_(long long a, long long m){long long x, y;extgcd_ntt_(a, m, x, y);return (m + x % m) % m;}long long garner_ntt_(int r0, int r1, int r2, int mod){using mint2 = ModInt<nttprimes[2]>;static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();static const long long m01_inv_m2 = mint2(m01).inv();int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;}template <typename MODINT>std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner){int sz = 1, n = a.size(), m = b.size();while (sz < n + m) sz <<= 1;if (sz <= 16) {std::vector<MODINT> ret(n + m - 1);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];}return ret;}int mod = MODINT::get_mod();if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)){a.resize(sz), b.resize(sz);if (a == b) { ntt(a, false); b = a; }else ntt(a, false), ntt(b, false);for (int i = 0; i < sz; i++) a[i] *= b[i];ntt(a, true);a.resize(n + m - 1);}else {std::vector<int> ai(sz), bi(sz);for (int i = 0; i < n; i++) ai[i] = a[i].val;for (int i = 0; i < m; i++) bi[i] = b[i].val;auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);a.resize(n + m - 1);for (int i = 0; i < n + m - 1; i++) {a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);}}return a;}int main(){int N, K;cin >> N >> K;vector<mint> x(K + 1);IREP(i, x.size()) x[i] = mint(mint(i).power(N)) * (i % 2 ? -1 : 1) / mint(i).fac();vector<mint> k(K + 1);REP(i, k.size()) k[i] = 1 / mint(i).fac();vector<mint> y = nttconv(x, k);mint ret = 0;FOR(i, 1, K + 1) if ((K - i) % 2) ret += mint(i).fac() * (i % 2 ? -1 : 1) * y[i] * mint(K).nCr(i);cout << ret << '\n';}