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>
using namespace std;
long long d[101][100001],i,j,n,k,a[101],mod=1e9+7;
int main()
{
    cin>>n>>k;
    for(i=1;i<=n;i++) cin>>a[i];
    d[0][0]=1;
    for(i=1;i<=n;i++){
        d[i][0]=d[i-1][0];
        for(j=1;j<=k;j++) d[i-1][j]+=d[i-1][j-1];
        for(j=1;j<=k;j++){
            if(j-a[i]-1>=0) d[i][j]-=d[i-1][j-a[i]-1];
            d[i][j]+=d[i-1][j]+mod+mod;
            d[i][j]%=mod;
        }

    }
    cout<<d[n][k];
    return 0;
}
