Codeforces Round #258 (Div. 2) E . Devu and Flowers 母函数+公式

题解：http://codeforces.com/blog/entry/13181

#include<stdio.h>
#include<string.h>
#include<math.h>
#include<iostream>
#include<algorithm>
using namespace std;
#define N 55
#define ll long long
#define inf 0x3f3f3f3f

ll mod=1e9+7;
ll f[22];
ll n,s;
ll inv(ll a)//求逆元
{
	return a == 1 ? 1 : (long long)(mod - mod / a) * inv(mod % a) % mod;
}
ll choose(ll m,ll k)求组合数C(m,k)
{
	ll ret=1;
	for(ll i=0;i<k;i++)
		ret=ret*((m-i)%mod)%mod*inv(i+1)%mod;
	return ret;
}
ll go(ll i,ll s)//求解系数
{
	if(s<0) return 0;
	if(i==n)
		return choose(n+s-1,n-1);
	return (go(i+1,s)-go(i+1,s-f[i])+mod)%mod;
}
int main()
{
	cin>>n>>s;
	for(int i=0;i<n;i++)
	{
		cin>>f[i];
		f[i]++;
	}
	cout<<(go(0,s)+mod)%mod<<endl;
	//system("pause");
}