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;
const int md = 1e9+7;
long long n, k, a, b[105][100005];

int main(){
    scanf("%lld%lld", &n, &k);
    fill(b[0],b[0]+k+1,1);
    for(int i = 0; i < n; i++){
        scanf("%lld", &a);
        b[i+1][0] = 1;
        for(int j = 1; j <= k; j++){
            b[i+1][j] = (b[i][j] - b[i][j-a-1<0 ? k+1 : j-a-1] + b[i+1][j-1] + md) % md;
        }
    }
    printf("%lld\n", (b[n][k] - b[n][k-1<0 ? k+1 : k-1] + md) % md);
}