結果

問題 No.1100 Boxes
ユーザー ningenMeningenMe
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
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ファイルパターン 結果
sample AC * 4
other AC * 36
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ソースコード

diff # 

#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;
}
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