結果
問題 | No.1100 Boxes |
ユーザー |
|
提出日時 | 2020-06-27 19:09:18 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 162 ms / 2,000 ms |
コード長 | 10,473 bytes |
コンパイル時間 | 4,192 ms |
コンパイル使用メモリ | 204,500 KB |
最終ジャッジ日時 | 2025-01-11 12:57:55 |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
(要ログイン)
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 ll = long long;#define ALL(obj) (obj).begin(),(obj).end()#define SPEED cin.tie(0);ios::sync_with_stdio(false);template<class T> using PQ = priority_queue<T>;template<class T> using PQR = priority_queue<T,vector<T>,greater<T>>;constexpr long long MOD = (long long)1e9 + 7;constexpr long long MOD2 = 998244353;constexpr long long HIGHINF = (long long)1e18;constexpr long long LOWINF = (long long)1e15;constexpr long double PI = 3.1415926535897932384626433L;template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "")<< obj[i]; o << "}"; return o;}template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}template <template <class tmp> class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}void print(void) {cout << endl;}template <class Head> void print(Head&& head) {cout << head;print();}template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}template <class T> void chmax(T& a, const T b){a=max(a,b);}template <class T> void chmin(T& a, const T b){a=min(a,b);}void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}/** @title NumberTheoreticTransform*/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);//互いに素になるように処理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;}};//Pow_Mod O(log(n))long long PowMod(long long x, long long n, long long mod) {long long res = 1;for (; n > 0; n >>= 1, (x *= x) %= mod) if (n & 1) (res *= x) %= mod;return res;}//Inv_Mod O(log(mod))long long InvMod(long long x, long long mod){return PowMod(x,mod-2,mod);}/** @title CombinationMod*/template<long long mod> class CombinationMod {vector<long long> fac,finv,inv;public:CombinationMod(int N) : fac(N + 1), finv(N + 1), inv(N + 1) {fac[0] = fac[1] = finv[0] = finv[1] = inv[1] = 1;for (int i = 2; i <= N; ++i) {fac[i] = fac[i - 1] * i % mod;inv[i] = mod - inv[mod%i] * (mod / i) % mod;finv[i] = finv[i - 1] * inv[i] % mod;}}inline long long binom(int n, int k) {return ((n < 0 || k < 0 || n < k) ? 0 : fac[n] * (finv[k] * finv[n - k] % mod) % mod);}inline long long factorial(int n) {return fac[n];}};/** @title ModInt*/template<long long mod> class ModInt {public:long long x;constexpr ModInt():x(0) {// do nothing}constexpr ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {// do nothing}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator+=(const long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator+=(const int y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}ModInt operator-() const { return ModInt(-x); }ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}ModInt operator--() {x--;if(x<0) x+=mod;return *this;}ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }ModInt operator^(const ModInt &p) const { return ModInt(*this) ^= p; }bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inv() const {int a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ModInt(u);}ModInt pow(long long n) const {ModInt ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt &a) {long long t;is >> t;a = ModInt<mod>(t);return (is);}};using modint = ModInt<MOD2>;int main() {ll N,K; cin >> N >> K;CombinationMod<MOD2> CM(K);vector<ll> a(K+1,0),b(K+1,0);for(ll i = 1; i <= K; i += 2) {a[i] = InvMod(CM.factorial(i),MOD2);}for(ll i = 0; i <= K; ++i) {b[i] = ((1-(i%2)*2)*InvMod(CM.factorial(i),MOD2)+MOD2)%MOD2;}auto c = NumberTheoreticTransform<MOD2>::convolution(a,b);modint ans = 0;for(ll i = 0; i <= K; ++i) {modint cnt = CM.factorial(K);cnt *= c[i];cnt *= PowMod(K-i,N,MOD2);cnt *= InvMod(CM.factorial(K-i),MOD2);ans += cnt;}cout << ans << endl;return 0;}