Submission #34911294

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Source Code Expand

#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<random>
#include<assert.h>
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n';
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n';
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pil>vpil;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
	r=0;bool w=0;char ch=getchar();
	while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
	while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
	return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
int mod;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
int qpow(int x,int y,int mod=mod){
	int s=1;
	while(y){
		if(y&1)s=1ll*s*x%mod;
		x=1ll*x*x%mod;
		y>>=1;
	}
	return s;
}
const int N=3010;
int n;
int S[N][N],C[N][N];
int solve(int x){
	int y=n-x,t=qpow(2,y),tmp=1;
	int s=0;
	for(int j=0;j<=x;j++){
		cadd(s,1ll*tmp*add(1ll*(j+1)*S[x][j+1]%mod,S[x][j])%mod);
		tmp=1ll*tmp*t%mod;
	}
	return 1ll*s*qpow(2,qpow(2,y,mod-1))%mod;
}
signed main(){
	#ifdef do_while_true
//		assert(freopen("data.in","r",stdin));
//		assert(freopen("data.out","w",stdout));
	#endif
	read(n,mod);
	S[0][0]=C[0][0]=1;
	for(int i=1;i<=n+1;i++){
		C[i][0]=1;
		for(int j=1;j<=i;j++){
			C[i][j]=add(C[i-1][j-1],C[i-1][j]);
			S[i][j]=add(S[i-1][j-1],1ll*j*S[i-1][j]%mod);
		}
	}
	int ans=0;
	for(int i=0;i<=n;i++){
		if(i&1)cdel(ans,1ll*C[n][i]*solve(i)%mod);
		else cadd(ans,1ll*C[n][i]*solve(i)%mod);
	}
	cout << ans << '\n';
    #ifdef do_while_true
		cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
	#endif
	return 0;
}

Submission Info

Judge Result