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 N = 3e3 + 10;
const int MOD = 1e9 + 7;
 
typedef long long ll;
int main() {
    int n, k;
    cin >> n >> k;
    vector<ll> f(k + 1, 1);
    while (n--) {
        int use;
        cin >> use;
        for(int i = k; i >= 0; i--) {
            f[i] -= (i - use - 1 >= 0 ? f[i - use - 1] : 0);
        }
        for(int i = 1; i <= k; i++)
            f[i] = (f[i] + f[i - 1] + 2LL * MOD) % MOD;
    }
    ll ans = f[k];
    if (k > 0) ans = (ans - f[k - 1] + MOD) % MOD;
    cout << ans;
}
