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;
int main(){
  int n,k;
  cin>>n>>k;
  vector<int> a(n);
  for(int i=0;i<n;i++)
    cin>>a.at(i);
  vector<vector<int>> dp(k+1,vector<int>(n+1,0));
  int p=1000000007;
  for(int j=0;j<=n;j++)
    dp[0][j]=1;
  for(int i=1;i<=k;i++){
    for(int j=1;j<=n;j++){
      dp[i][j]=(dp[i-1][j]+dp[i][j-1])%p;
      if(i-a.at(j-1)-1>=0)
        dp[i][j]=(dp[i][j]-dp[i-a.at(j-1)-1][j-1]+p)%p;
    }
  }
  cout<<dp[k][n]<<endl;
}