Codeforces Round #258 E Devu and Flowers --容斥原理

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#define Mod 1000000007
#define lll __int64
#define ll long long
using namespace std;
#define N 100007

ll a[22];
ll inv[30];

ll fastm(ll a,ll b)
{
    ll res = 1LL;
    while(b)
    {
        if(b&1LL)
            res = (res*a)%Mod;
        b >>= 1;
        a = (a*a)%Mod;
    }
    return res;
}

ll comb(ll n,ll r)
{
    if(r > n)
        return 0;
    r = min(r,n-r);
    n%=Mod;
    ll ans = 1LL;
    for(int i=0;i<=r-1;i++)
    {
        ans = ans*(n-i)%Mod;
        ans = ans*inv[i+1]%Mod;
    }
    return ans;
}

int calc(int s)
{
    int cnt = 0;
    while(s)
    {
        if(s&1)
            cnt++;
        s >>= 1;
    }
    return cnt;
}

int main()
{
    int n,i;
    ll s;
    for(i=1;i<=30;i++)
        inv[i] = fastm(i,Mod-2);
    while(cin>>n>>s)
    {
        for(i=0;i<n;i++)
            cin>>a[i];
        ll ans = 0;
        int S = (1<<n)-1;
        for(int state=0;state<=S;state++)
        {
            ll r = s;
            int tmp = state;
            int cnt = calc(state);
            i=0;
            while(i<n)
            {
                if(tmp&1)
                    r -= (a[i]+1);
                tmp >>= 1;
                i++;
            }
            if(r < 0)
                continue;
            ll cb = comb(n+r-1,r);
            if(cnt%2)
                cb = -cb;
            ans = (ans+cb+Mod)%Mod;
        }
        printf("%I64d\n",ans);
    }
    return 0;
}