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 MOD = 1e9 + 7;

int main(){
  int n, k;
  cin >> n >> k;
  vector<int> pref(k+1), dp(k+1);
  dp[0] = 1;
  for(int kid = 1;kid<=n;kid++){
    int c;
    cin >> c;
    pref[0] = dp[0];
    for(int i = 1;i<=k;i++)
      pref[i] = (pref[i-1] + dp[i]) % MOD;
    for(int i = 0;i<=k;i++)
      dp[i] = (pref[i] - (i-c>=0 ? pref[i-c-1] : 0)) % MOD;
  }

  int ans = dp[k];
  if(ans < 0) ans += MOD; 
  printf("%d\n",ans);

  return 0;
}
