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 <iostream>
using namespace std;

const int N = 101, K = 1e5 + 1, MOD = 1e9 + 7;

int n, k, val[N], pos[K];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  
  cin >> n >> k;
  
  for(int i = 0; i < n; i++)
    cin >> val[i];
  
  pos[0] = 1;
  for(int i = 0; i < n; i++) {
    int d = k, sum = 0;
    for(int f = k; f > -1; f--) {
      sum = (sum - pos[f] + MOD) % MOD;
      while(d > -1 && f - d <= val[i])
        sum = (sum + pos[d--]) % MOD;
      pos[f] = (pos[f] + sum) % MOD;
    }
  }
  cout << pos[k];
}