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 <cstdio>
#include <algorithm>

int n, k;
int A[100];

constexpr int mod = 1000000007;
int dp[101][100001];

int main(){
  scanf("%d%d", &n, &k);
  for(int i = 0; i < n; i++) scanf("%d", A+i);
  dp[0][0] = 1;
  for(int i = 1; i <= n; i++){
    int sum[100001];
    for(int j = 0; j <= k; j++){
      sum[j] = (j ? sum[j-1] : 0) + dp[i-1][j];
      if(sum[j] >= mod) sum[j] -= mod;
      dp[i][j] = sum[j] + (A[i-1] >= j ? 0 : mod - sum[j-A[i-1]-1]);
      if(dp[i][j] >= mod) dp[i][j] -= mod;
    }
  }
  printf("%d\n", dp[n][k]);
  return 0;
}
