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 main() {
    int m = 1e9 + 7;
    int n, k, c;
    cin>>n>>k;

    vector<int> dp(k+1, 1);
    while(n--) {
        cin>>c;
        for(int i=k; i>=0; i--)
            dp[i] = (dp[i] + m - (i-c > 0 ? dp[i-c-1] : 0)) % m;
        for(int i=1; i<=k; i++) dp[i] = (dp[i] + dp[i-1]) % m;
    }
    if(k == 0) cout << dp[k] << endl;
    else cout << (dp[k] + m - dp[k-1]) % m << endl;

    return 0;
}