Luogu P3270 [JLOI2016]成绩比较

Luogu P3270 [JLOI2016]成绩比较
很妙的拆式子，见小本本

#include<bits/stdc++.h>
#define ll long long
const int p=1e9+7;
using namespace std;

const int N=105;
int K,n,m,U[N],r[N];
ll c[N][N],f[N],inv[N],pre[N],suf[N];
inline int ksm(ll a,int b) {
	ll ret=1;
	while(b) {
		if(b&1) ret=ret*a%p;
		a=a*a%p,b>>=1;
	}
	return ret;
}
inline int mo(int x) {
	return x>=p?x-p:x;
}
inline int ask(ll *f,int k,int x) {
	if(x<=k) return f[x]; 
	pre[0]=x;
	for(int i=1;i<=k;i++) {
		pre[i]=pre[i-1]*(x-i)%p;
	}
	suf[k]=x-k;
	for(int i=k-1;i>=0;i--) {
		suf[i]=suf[i+1]*(x-i)%p;
	}
	ll ret=0;
	for(int i=0;i<=k;i++) {
		ll s=f[i]*inv[k-i]%p*inv[i]%p;
		if(i) s=s*pre[i-1]%p;
		if(i<k) s=s*suf[i+1]%p;
		if((k-i)&1) s=-s; 
		ret=(ret+s)%p;
	}
	return (ret+p)%p;
}
int main() {
	scanf("%d%d%d",&n,&m,&K);
	for(int i=1;i<=m;i++) scanf("%d",&U[i]);
	for(int i=1;i<=m;i++) scanf("%d",&r[i]);
	inv[0]=inv[1]=1;
	for(int i=2;i<=n+1;i++) inv[i]=(p-p/i)*inv[p%i]%p;
	for(int i=2;i<=n+1;i++) inv[i]=inv[i]*inv[i-1]%p;
	c[0][0]=1;
	for(int j=1;j<=n;j++) {
		c[0][j]=1;
		for(int i=1;i<=j;i++) {
			c[i][j]=(c[i-1][j-1]+c[i][j-1])%p;
		}
	}
	ll ans=c[K][n-1],sum=0;
	for(int i=0;i<=n-K-1;i++) {
		ll t=c[i][n-K-1];
		for(int j=1;j<=m;j++) {
			t=t*c[r[j]-1][n-K-1-i]%p;
		}
		if(i&1) sum=(sum-t)%p;
			else sum=(sum+t)%p;
	}
	ans=ans*sum%p;
	for(int i=1;i<=m;i++) {
		ll sum=0;
		for(int k=0;k<=r[i]-1;k++) {
			ll t=c[k][r[i]-1]*ksm(U[i],k)%p;
			memset(f,0,sizeof(f));
			for(int j=1;j<=n-k;j++) {
				f[j]=mo(f[j-1]+ksm(j,n-k-1));
			}
			t=t*ask(f,n-k,U[i])%p;
			if((r[i]-k+1)&1) {
				sum=(sum-t)%p;
			} else sum=(sum+t)%p;
		}
		ans=ans*sum%p;
	}
	printf("%lld\n",(ans+p)%p); 
	return 0;
}