結果

問題 No.1783 Remix Sum
ユーザー sigma425sigma425
提出日時 2021-12-14 08:41:57
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 6,200 ms / 10,000 ms
コード長 13,285 bytes
コンパイル時間 4,062 ms
コンパイル使用メモリ 220,968 KB
最終ジャッジ日時 2025-01-26 22:31:00
ジャッジサーバーID
（参考情報） 		judge3 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 76
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 # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}
	// ll extgcd(ll a,ll b,ll &x,ll &y) const{
	// 	ll p[]={a,1,0},q[]={b,0,1};
	// 	while(*q){
	// 		ll t=*p/ *q;
	// 		rep(i,3) swap(p[i]-=t*q[i],q[i]);
	// 	}
	// 	if(p[0]<0) rep(i,3) p[i]=-p[i];
	// 	x=p[1],y=p[2];
	// 	return p[0];
	// }
	// ModInt inv() const {
	// 	ll x,y;
	// 	extgcd(v,mod,x,y);
	// 	return make(normS(x+mod));
	// }

	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	bool operator<(const ModInt& b) const { return v<b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<120586241>;

// inplace_fmt (without bit rearranging)
// fft:
// 		a[rev(i)] <- \sum_j \zeta^{ij} a[j]
// invfft:
//		a[i] <- (1/n) \sum_j \zeta^{-ij} a[rev(j)]
// These two are inversions.


// !!! CHANGE IF MOD is unusual !!!
const int ORDER_2_MOD_MINUS_1 = 20;	// ord_2 (mod-1)
const mint PRIMITIVE_ROOT = 6; // primitive root of (Z/pZ)*

void fft(V<mint>& a){
	static constexpr uint mod = mint::mod;
	static constexpr uint mod2 = mod + mod;
	static const int H = ORDER_2_MOD_MINUS_1;
	static const mint root = PRIMITIVE_ROOT;
	static mint magic[H-1];

	int n = si(a);
	assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H);	// n should be power of 2

	if(!magic[0]){		// precalc
		rep(i,H-1){
			mint w = -root.pow(((mod-1)>>(i+2))*3);
			magic[i] = w;
		}
	}
	int m = n;
	if(m >>= 1){
		rep(i,m){
			uint v = a[i+m].v;					// < M
			a[i+m].v = a[i].v + mod - v;		// < 2M
			a[i].v += v;						// < 2M
		}
	}
	if(m >>= 1){
		mint p = 1;
		for(int h=0,s=0; s<n; s += m*2){
			for(int i=s;i<s+m;i++){
				uint v = (a[i+m] * p).v;		// < M
				a[i+m].v = a[i].v + mod - v;	// < 3M
				a[i].v += v;					// < 3M
			}
			p *= magic[__builtin_ctz(++h)];
		}
	}
	while(m){
		if(m >>= 1){
			mint p = 1;
			for(int h=0,s=0; s<n; s += m*2){
				for(int i=s;i<s+m;i++){
					uint v = (a[i+m] * p).v;		// < M
					a[i+m].v = a[i].v + mod - v;	// < 4M
					a[i].v += v;					// < 4M
				}
				p *= magic[__builtin_ctz(++h)];
			}
		}
		if(m >>= 1){
			mint p = 1;
			for(int h=0,s=0; s<n; s += m*2){
				for(int i=s;i<s+m;i++){
					uint v = (a[i+m] * p).v;								// < M
					a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;	// < 2M
					a[i+m].v = a[i].v + mod - v;							// < 3M
					a[i].v += v;											// < 3M
				}
				p *= magic[__builtin_ctz(++h)];
			}
		}
	}
	rep(i,n){
		a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;		// < 2M
		a[i].v = (a[i].v >= mod) ? a[i].v - mod : a[i].v;		// < M
	}
	// finally < mod !!
}
void invfft(V<mint>& a){
	static constexpr uint mod = mint::mod;
	static constexpr uint mod2 = mod + mod;
	static const int H = ORDER_2_MOD_MINUS_1;
	static const mint root = PRIMITIVE_ROOT;
	static mint magic[H-1];

	int n = si(a);
	assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H);	// n should be power of 2

	if(!magic[0]){		// precalc
		rep(i,H-1){
			mint w = -root.pow(((mod-1)>>(i+2))*3);
			magic[i] = w.inv();
		}
	}
	int m = 1;
	if(m < n>>1){
		mint p = 1;
		for(int h=0,s=0; s<n; s += m*2){
			for(int i=s;i<s+m;i++){
				ull x = a[i].v + mod - a[i+m].v;	// < 2M
				a[i].v += a[i+m].v;					// < 2M
				a[i+m].v = (p.v * x) % mod;			// < M
			}
			p *= magic[__builtin_ctz(++h)];
		}
		m <<= 1;
	}
	for(;m < n>>1; m <<= 1){
		mint p = 1;
		for(int h=0,s=0; s<n; s+= m*2){
			for(int i=s;i<s+(m>>1);i++){
				ull x = a[i].v + mod2 - a[i+m].v;	// < 4M
				a[i].v += a[i+m].v;					// < 4M
				a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v;	// < 2M
				a[i+m].v = (p.v * x) % mod;		// < M
			}
			for(int i=s+(m>>1); i<s+m; i++){
				ull x = a[i].v + mod - a[i+m].v;	// < 2M
				a[i].v += a[i+m].v;	// < 2M
				a[i+m].v = (p.v * x) % mod;	// < M
			}
			p *= magic[__builtin_ctz(++h)];
		}
	}
	if(m < n){
		rep(i,m){
			uint x = a[i].v + mod2 - a[i+m].v;	// < 4M
			a[i].v += a[i+m].v;	// < 4M
			a[i+m].v = x;	// < 4M
		}
	}
	const mint in = mint(n).inv();
	rep(i,n) a[i] *= in;	// < M
	// finally < mod !!
}

/*
	h[i1+j1][i2+j2]..[ik+jk] += f[i1][i2]..[ik] * g[i1][i2]..[ik] をする
	ただし 添字の範囲は 0 <= ip,jp < np で、足した結果一箇所でもはみ出た値は捨てる
	f,g は flatten されている (i1,i2,..,ik) が i1 + i2n1 + i3n1n2 + .. に対応する
	magicはcalc_magicで計算したのを使う

	O(knlogn)
	各次元を2倍にして愚直にやるとO(2^k nlogn) とかになるはずで、すげ～
*/
V<int> calc_magic(const vector<int>& ns){
	int k = si(ns);
	if(k == 0) return {};
	int n = 1;
	for(int ni: ns) n *= ni;
	V<int> magic(n);
	rep(i,n){
		int x = i;
		rep(j,k){
			magic[i] += x;
			x /= ns[j];
		}
		magic[i] %= k;
	}
	return magic;
}
vector<mint> multivariate_mult(const vector<mint>& f, const vector<mint>& g, const vector<int>& ns, const vector<int>& magic){
	assert(si(f) == si(g));
	int n = si(f);
	int k = si(ns);
	if(k == 0){
		return {f[0]*g[0]};
	}
	int s = 1; while(s<n*2-1) s*=2;
	vector<mint> h(n);
	vector<vector<mint>> zf(k,vector<mint>(s));
	vector<vector<mint>> zg(k,vector<mint>(s));
	vector<vector<mint>> zh(k,vector<mint>(s));
	rep(i,n) zf[magic[i]][i] = f[i];
	rep(i,k) fft(zf[i]);
	rep(i,n) zg[magic[i]][i] = g[i];
	rep(i,k) fft(zg[i]);
	rep(a,k) rep(b,k){
		int c = (a+b)%k;
		rep(i,s) zh[c][i] += zf[a][i] * zg[b][i];
	}
	rep(i,k) invfft(zh[i]);
	rep(i,n) h[i] = zh[magic[i]][i];
	return h;
}

vector<mint> multivariate_log(const vector<mint>& f, const vector<int>& ns, const vector<int>& magic){
	exit(1);
}

V<int> tens = {1,10,100,1000,10000,100000};
V<mint> zs;
vector<mint> mult(vector<mint> f, vector<mint> g, int A,int B, bool za, bool zb, bool zc){
	int n = si(f);

	auto zeta10 = [&](V<mint> f){
		V<mint> g(10);
		rep(i,10) rep(j,10) g[i] += f[j] * zs[i*j];
		return g;
	};
	auto izeta10 = [&](V<mint> f){
		const static mint i10 = mint(10).inv();
		V<mint> g(10);
		rep(i,10) rep(j,10) g[i] += f[j] * zs[90-i*j] * i10;
		return g;
	};
	auto zeta = [&](vector<mint> f){
		for(int d=A;d<A+B;d++){	// cyclic DFTed dim
			rep(s,n) if(s/tens[d]%10 == 0){
				V<mint> buf(10);
				rep(i,10) buf[i] = f[s+tens[d]*i];
				buf = zeta10(buf);
				rep(i,10) f[s+tens[d]*i] = buf[i];
			}
		}
		return f;
	};
	auto izeta = [&](vector<mint> f){
		for(int d=A;d<A+B;d++){	// cyclic DFTed dim
			rep(s,n) if(s/tens[d]%10 == 0){
				V<mint> buf(10);
				rep(i,10) buf[i] = f[s+tens[d]*i];
				buf = izeta10(buf);
				rep(i,10) f[s+tens[d]*i] = buf[i];
			}
		}
		return f;
	};
	if(!za) f = zeta(f);
	if(!zb) g = zeta(g);
	V<mint> zf(tens[A]), zg(tens[A]),zh;
	V<int> ns(A,10); V<int> magic = calc_magic(ns);
	rep(s,si(f)) if(s%tens[A] == 0){
		rep(i,tens[A]) zf[i] = f[s+i], zg[i] = g[s+i];
		zh = multivariate_mult(zf,zg,ns,magic);
		// show(zf);show(zg);show(zh);
		// show(ns);show(magic);
		// show("------------");
		rep(i,tens[A]) f[s+i] = zh[i];
	}
	if(!zc) f = izeta(f);
	return f;
}

template <class T, class Op = multiplies<>>
constexpr T power(T a, uint64_t n, T init = 1, Op op = Op{}) {
	while (n) {
		if (n & 1) init = op(init, a);
		if (n >>= 1) a = op(a, a);
	}
	return init;
}



int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);

	int N,A,B; ll X;
	{
		int K;
		cin >> N;
		cin >> K;
		cin >> X;
		int T;
		cin >> T;
		A = T, B = K-T;
	}

	{
		mint z = mint(6).pow((mint::mod-1)/10);
		rep(i,91) zs.pb(z.pow(i));
	}

	V<mint> f(TEN(A+B));
	while(N--){
		int x; cin >> x; f[x]++;
	}
	auto mul = [&](auto x,auto y,bool za,bool zb,bool zc){ return mult(x,y,A,B,za,zb,zc); };
	V<mint> id(TEN(A+B)); id[0] = 1;
	// f = power(f,X,id,mul);
	// for(auto v: f) cout << v << endl;

	V<mint> f0(TEN(A+B)),f1(TEN(A+B));
	rep(s,TEN(A+B)){
		if(s%TEN(A) == 0) f0[s] = f[s];
		else f1[s] = f[s];
	}

	ll XX = max(X-45,0LL);
	ll work = X-XX;
	VV<mint> f1pow(work+1);
	f1pow[0] = id;
	rep1(i,work) f1pow[i] = mul(f1pow[i-1], f1, 0,0,0);

	int n = si(f);
	auto zeta10 = [&](V<mint> f){
		V<mint> g(10);
		rep(i,10) rep(j,10) g[i] += f[j] * zs[i*j];
		return g;
	};
	auto izeta10 = [&](V<mint> f){
		const static mint i10 = mint(10).inv();
		V<mint> g(10);
		rep(i,10) rep(j,10) g[i] += f[j] * zs[90-i*j] * i10;
		return g;
	};
	auto zeta = [&](vector<mint> f){
		for(int d=A;d<A+B;d++){	// cyclic DFTed dim
			rep(s,n) if(s/tens[d]%10 == 0){
				V<mint> buf(10);
				rep(i,10) buf[i] = f[s+tens[d]*i];
				buf = zeta10(buf);
				rep(i,10) f[s+tens[d]*i] = buf[i];
			}
		}
		return f;
	};
	auto izeta = [&](vector<mint> f){
		for(int d=A;d<A+B;d++){	// cyclic DFTed dim
			rep(s,n) if(s/tens[d]%10 == 0){
				V<mint> buf(10);
				rep(i,10) buf[i] = f[s+tens[d]*i];
				buf = izeta10(buf);
				rep(i,10) f[s+tens[d]*i] = buf[i];
			}
		}
		return f;
	};
	show(f0);
	show(f1);
	show(f1pow);
	show(XX);

	VV<mint> gs(work+1);
	if(true){
		auto g0 = zeta(f0);
		V<mint> g(TEN(A+B));
		rep(s,n) if(s%TEN(A) == 0) g[s] = g0[s].pow(XX);
		rep(i,work+1){
			gs[work-i] = g;
			rep(s,n) g[s] *= g0[s];
		}
	}
	show(gs);
	V<mint> ans(TEN(A+B));
	mint choose = 1;
	rep(i,work+1){
		// auto p = mul(f1pow[i],gs[i],0,1,1);
		V<mint> p;
		if(true){
			auto F = zeta(f1pow[i]);
			auto G = gs[i];
			show(F);show(G);
			rep(s,si(F)) if(s%tens[A] == 0){
				rep(i,tens[A]) F[s+i] *= G[s];
			}
			p = F;
		}

		rep(s,n) ans[s] += p[s] * choose;
		choose *= X-i;
		choose /= i+1;
	}
	ans = izeta(ans);
	rep(s,n) cout << ans[s] << endl;
}
0