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 DIM 107
#define modulo 1000000007
using namespace std;

long long n,k,a[DIM],p[DIM][100007];

int main()
{
    cin>>n>>k;
    for(int i = 1; i <= n; ++i)
        cin>>a[i];

    for(int i = 0; i <= k; ++i)
        p[0][i] = 1;

    for(int i = 1; i <= n; ++i)
        for(int j = 0; j <= k; ++j)
    {
        p[i][j] = p[i][j-1] + p[i-1][j];
        if(a[i]<j) p[i][j]-=p[i-1][j-a[i]-1];
        p[i][j]+=modulo;
        p[i][j]%=modulo;
    }

    cout<<(p[n][k]-p[n][k-1]+modulo)%modulo;
    return 0;
}
