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;
using ii = long long;
const ii mod = 1e9+7;
ii _dp[2][100100];
#define dp _dp[z]
#define pd _dp[!z]
int main()
{
    int n, k, z = 1;
    cin >> n >> k;
    dp[0] = 1;
    for (int i = 1; i <= n; ++i) {
        z = !z;
        int x;
        cin >> x;
        ii s = 0;
        for (int j = 0; j <= k; ++j) {
            s += pd[j];
            s %= mod;
            dp[j] = s;
            if (j >= x) {
                s = (s - pd[j - x] + mod) % mod;
            }
        }
    }
    cout << dp[k] << "\n";
}
