There are N children, numbered 1, 2, \ldots, N.

They have decided to share K candies among themselves. Here, for each i (1 \leq i \leq N), Child i must receive between 0 and a_i candies (inclusive). Also, no candies should be left over.

Find the number of ways for them to share candies, modulo 10^9 + 7. Here, two ways are said to be different when there exists a child who receives a different number of candies.

Constraints

* All values in input are integers.
* 1 \leq N \leq 100
* 0 \leq K \leq 10^5
* 0 \leq a_i \leq K

Input

Input is given from Standard Input in the following format:


N K
a_1 a_2 \ldots a_N


Output

Print the number of ways for the children to share candies, modulo 10^9 + 7.

Examples

Input

3 4
1 2 3


Output

5


Input

1 10
9


Output

0


Input

2 0
0 0


Output

1


Input

4 100000
100000 100000 100000 100000


Output

665683269
#include<bits/stdc++.h>
#define REP(i,n) for(int i=0,i##_len=(n);i<i##_len;++i)
#define int long long
using namespace std;
typedef pair<int,int> P;
constexpr int mod=1e9+7;
int N,K;
int a[100];
int dp[101][200002]={};

signed main(){
    cin>>N>>K;
    REP(i,N) cin>>a[i];
    dp[N][K]=1;
    for(int i=N-1;i>=0;--i) for(int j=K;j>=0;--j){
        dp[i][j]=dp[i+1][j]+dp[i][j+1]-dp[i+1][j+a[i]+1];
        dp[i][j]=(dp[i][j]+mod)%mod;
    }
    cout<<dp[0][0]<<endl;
}
