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;
int n , TotalK , a[110];
long long dp[101][100010] , mod = 1e9 + 7;

int main()
{
    cin >> n >> TotalK;
    for(int i = 0 ; i < n ; i++)    cin >> a[i];

    dp[n][0] = 1;
    for(int i = n-1 ; i >= 0 ; i--)
        for(int k = 0 ; k <= TotalK ; k++)
            dp[i][k] = ((dp[i+1][k] + (k?dp[i][k-1]:0))%mod + (k > a[i] ? mod - dp[i+1][k-a[i]-1] : 0))%mod;
    cout << dp[0][TotalK] << '\n';
    return 0;
}
