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>

const int MOD=1e9+7;

int N,K;

int dp[100005];

int main(){
  scanf("%d %d",&N,&K);
  dp[0]=1;
  for(int t=0;t<N;t++){
    int A;
    scanf("%d",&A);
    for(int i=1;i<=K;i++){
      dp[i]=(dp[i]+dp[i-1])%MOD;
    }
    for(int i=K;i>A;i--){
      dp[i]=(dp[i]-dp[i-A-1])%MOD;
    }
  }
  printf("%d\n",(dp[K]+MOD)%MOD);
  return 0;
}
