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>
#define rep(i, n) for(int i=0; i<(n); i++)
using namespace std;

int main(){
  int n, k; cin >> n >> k;
  int a[n];
  rep(i, n) cin >> a[i];
  long mod = 1e9 + 7;
  long dp[n+1][k+1];
  long s[n+1][k+2];
  rep(i, k+1) dp[0][i] = 0;
  dp[0][0] = 1;
  rep(i, k+2) s[0][i] = 1;
  rep(i, n+1) s[i][0] = 0;
  for(int i=1; i<n+1; i++){
    rep(j, k+1){
      dp[i][j] = (s[i-1][j+1] - s[i-1][max(0, j-a[i-1])] + mod) % mod;
      s[i][j+1] = (s[i][j] + dp[i][j]) % mod;
    }
  }
  cout << dp[n][k] << endl;
}