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 MOD = 1000000007;
int main()
{
    int N, K; cin >> N >> K;
    vector<int> A(K+1);
    A[0] = 1;
    for (int i = 0; i < N; i++) {
        int a; cin >> a;
        vector<long long> B(K+1);
        B[0] = A[0];
        for (int j = 1; j <= K; j++) {
            B[j] = B[j-1] + A[j];
        }
        for (int j = K; j >= 0; j--) {
            int lo = max(0, j - a);
            int hi = j;
            A[j] = (B[hi] - B[lo] + A[lo]) % MOD;
        }
    }
    cout << A[K] << endl;
    return 0;
}