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;
using ll = long long;
const ll mod = 1e9+7;
int main(){
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n,k,a;
  cin >> n >> k;
  vector<ll> cnt(k+1);
  cnt[0] = 1;
  for(int i = 0; i < n; ++i){
    cin >> a;
    ll tmp = 0;
    for(int j = k; j >= k-a; --j) tmp = (tmp+cnt[j])%mod;
    for(int j = k; j > 0; --j){
      tmp = (tmp-cnt[j])%mod;
      cnt[j] = (cnt[j]+tmp)%mod;
      if(j-a > 0) tmp = (tmp+cnt[j-a-1])%mod;
    }
  }
  cout << (cnt[k]+mod)%mod;
  return 0;
}