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| #include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<ctime>
#include<iomanip>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#define gh() getchar()
#define underMax(x,y) ((x)>(y)?(x):(y))
#define underMin(x,y) ((x)<(y)?(x):(y))
typedef long long ll;
using namespace std;
const int MAXN=21;
const int Mod=1e9+7;
template<class T>
inline void underRead(T &x)
{
x=0;
char ch=gh(),t=0;
while(ch<'0'||ch>'9') t|=ch=='-',ch=gh();
while(ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+(ch^48),ch=gh();
if(t) x=-x;
}
ll A[MAXN];
int down=1;
inline int underQmi(int a,int k,int p)
{
int res=1;
while(k)
{
if(k&1) res=(ll)res*a%p;
a=(ll)a*a%p;
k>>=1;
}
return res;
}
inline int underC(ll a,ll b)
{
if(a<b) return 0;
int up=1;
for(ll i=a;i>a-b;--i) up=i%Mod*up%Mod;
return (ll)up*down%Mod;
}
int main()
{
ll n,m;
underRead(n),underRead(m);
for(int i=0;i<n;++i) underRead(A[i]);
for(int j=1;j<n;++j) down=(ll)j*down%Mod;
down=underQmi(down,Mod-2,Mod);
int res=0;
for(int i=0;i<1<<n;++i)
{
ll a=n+m-1,b=n-1;
int sign=1;
for(int j=0;j<n;++j)
if(i>>j&1)
{
sign*=-1;
a-=A[j]+1;
}
res=(res+underC(a,b)*sign)%Mod;
}
printf("%d",(res+Mod)%Mod);
return 0;
}
|