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>
#define int long long
using namespace std;
const int mod=1000000007;
signed main(){
  int N,K;
  cin>>N>>K;
  vector<int> A(N);
  for(int &i:A)
    cin>>i;
  vector<vector<int>> B(N+1,vector<int>(K+1,0));
  B[0][0]=1;
  for(int i=0;i<N;i++){
    for(int j=0;j<=K;j++){
      B[i+1][j]=(B[i+1][j]+B[i][j])%mod;
      if(j+A[i]+1<=K)
        B[i+1][j+A[i]+1]=(B[i+1][j+A[i]+1]-B[i][j]+mod)%mod;
    }
    for(int j=1;j<=K;j++)
      B[i+1][j]=(B[i+1][j]+B[i+1][j-1])%mod;
  }
  cout<<B[N][K]<<endl;
}