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 = pow(10,9)+7;
int main(){
  int N,K,a;
  cin >> N >> K;
  vector<int> cnt(K+1);
  cnt[0] = 1;
  for(int i = 0; i < N; ++i){
    cin >> a;
    int psum = 0;
    for(int k = K-1; k >= max(0,K-a); --k) psum = (psum+cnt[k])%MOD;
    cnt[K] = (cnt[K]+psum)%MOD;
    for(int j = K-1; j > 0; --j){
      psum = (psum-cnt[j])%MOD;
      if(j-a >= 0) psum = (psum+cnt[j-a])%MOD;
      cnt[j] = (cnt[j]+psum)%MOD;
    }
  }
  cout << (cnt[K]+MOD)%MOD;
  return 0;
}