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;
typedef long long ll;

ll mod = 1e9+7;

ll dp[101][100001];
ll a[100];
int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int j = 0; j <= k; j++)
    dp[0][j] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j <= k; j++) {
      dp[i][j] = (dp[i-1][j]-(j > a[i-1] ? dp[i-1][j-a[i-1]-1] : 0) + (j ? dp[i][j-1] : 0))%mod;
    }
  }
  cout << ((dp[n][k]-(k ? dp[n][k-1] : 0))%mod+mod)%mod << endl;
}
