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 M = 1e9 + 7;

int main() {
  ios::sync_with_stdio(0);
  cout.tie(0);
  cin.tie(0);

  int n, k;
  cin >> n >> k;

  vector<int> dp(k + 1, 0);
  dp[0] = 1;

  for (int i = 0; i < n; ++i) {
    int x;
    cin >> x;
    for (int j = 1; j <= k; ++j) dp[j] = (dp[j] + dp[j-1]) % M;
    vector<int> tmp(k + 1, 0);
    for (int j = 0; j <= k; ++j) {
      int l = j - x;;
      tmp[j]  = dp[j];
      if (l > 0) tmp[j] = (tmp[j] - dp[l-1] + M) % M;
    }
    swap(tmp, dp);
  }
  cout << dp[k] << '\n';
}
