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;
int main(){
  int n, k; cin >> n >> k;
  vector<int> f(k + 1, 0);
  const int mod = 1000000007;
  f[0] = 1;
  for(int i = 0; i < n; i++){
    int x; cin >> x;
    vector<int> nf(k + 1, 0);
    int sum = 0;
    for(int j = 0; j <= k; j++){
      sum += f[j]; if(sum >= mod) sum -= mod;
      if(j > x) {
        sum += mod - f[j - x - 1];
        if(sum >= mod) sum -= mod;
      }
      nf[j] = sum;
    }
    f = nf;
  }
  cout << f[k] << endl;
  return 0;
}
