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 <iostream>

using namespace std;

const int M = 1e9+7;
int n, k, a[100100], dp[110][100100];

int main()
{
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];

  dp[0][0] = 1;

  for (int i = 0; i < n; i++) {
    long long sum = 0;
    for (int j = 0; j <= k; j++) {
      sum += dp[i][j];
      if (j-a[i]-1 >= 0) sum -= dp[i][j-a[i]-1]-M;
      sum %= M;
      dp[i+1][j] = sum;
    }
  }

  cout << dp[n][k] << endl;
  return 0;
}