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

#if 1

#include <bits/stdc++.h>
using namespace std;
int n,m;
int x;
long long d[1000005];

int main()
{
    scanf("%d %d", &n, &m);
    d[m] = 1;
    while(n--)
    {
        scanf("%d",&x);
        for(int i = m;i >= 0;i--) d[i] += d[i+1];
        for(int i = 0;i < m;i++)
        {
            d[i] -= d[i+x+1];
            d[i] %= 1000000007;
        }
    }
    printf("%lld",d[0]);
}

#endif // 1++