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;
#define ll long long
ll MOD = 1e9+7;
ll A[101000];ll n,k;ll B[110][101000];
int main(){
      cin>>n>>k;ll a;
      for(ll j=0;j<=k;j++){
            B[0][j] = 0;
      }
      B[0][0] = 1;
      A[0] = 0;
      for(ll i=1;i<=n;i++){
            cin>>a;
            for(ll j=0;j<=k;j++){
                  A[j+1] = (A[j]+B[i-1][j])%MOD;
            }
            for(ll j=0;j<=k;j++){
                  B[i][j] = (A[j+1]-A[max(0LL,j-a)]+MOD)%MOD;
            }
      }
      cout<<B[n][k]<<endl;
      return 0;
}
