Submission #724117

#TimeUsernameProblemLanguageResultExecution timeMemory
724117amirhoseinfar1385Tents (JOI18_tents)C++17
100 / 100
466 ms71100 KiB
#include<bits/stdc++.h>
using namespace std;
const int maxn=3000+10;
long long fact[maxn],revfact[maxn],mp[maxn];
long long mod=1e9+7;
long long mypow(long long m,long long y){
	if(y==0){
		return 1;
	}	
	long long p=mypow(m,(y>>1));
	p*=p;
	p%=mod;
	if(y&1){
		p*=m;
		p%=mod;
	}
	return p;
}

void aval(){
	fact[0]=1;
	for(int i=1;i<maxn;i++){
		fact[i]=fact[i-1]*i;
		fact[i]%=mod;
	}
	revfact[maxn-1]=mypow(fact[maxn-1],mod-2);
	for(int i=maxn-2;i>=0;i--){
		revfact[i]=revfact[i+1]*(i+1)%mod;
	}
	mp[0]=1;
	for(int i=1;i<maxn;i++){
		mp[i]=mp[i-1]*4%mod;
	}	
}
long long dp[maxn][maxn];
long long c(int i,int j){
	if(i<0||j<0||j>i){
		return 0;
	}
	long long ret=fact[i]*revfact[j]%mod*revfact[i-j]%mod;
	return ret;
}
long long pre[maxn];

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	long long n,m;
	cin>>n>>m;
	aval();
	//cout<<"whhat "<<c(2,2)<<'\n';
	for(int i=0;i<=n;i++){
		for(int j=0;j<=m;j++){
			if(i==0){
				dp[i][j]=1;
				continue;
			}
			if(j==0){
				dp[i][j]=0;
				continue;
			}
			dp[i][j]=dp[i-1][j-1]*j%mod*4%mod;
			if(i>=2){
				dp[i][j]+=dp[i-2][j-1]*j%mod*(i-1)%mod;
			}
			dp[i][j]%=mod;
		}	
	}
	pre[0]=1;
	for(int i=1;i*2<=m;i++){
		pre[i]=pre[i-1];
		pre[i]*=c(m-(i-1)*2,2);
		pre[i]%=mod;
	}	
	long long res=0;
	for(int i=0;i<=n&&i*2<=m;i++){
		for(int j=0;j+i<=n;j++){
			if(i+j==0){
				continue;
			}	
			long long fake=c(n,i)*c(n-i,j)%mod*pre[i]%mod*dp[j][m-i*2]%mod;
			//cout<<i<<" "<<j<<" "<<c(n,i)<<" "<<c(n-i,j)<<" "<<pre[i]<<" "<<dp[j][m-i*2]<<" "<<fake<<"\n";
			res+=fake;
		}
	}
	res%=mod;
	cout<<res<<"\n";
}
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