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;
const int mod = 1e9+7;
int main()
{
  int n, k;
  cin>>n>>k;
  int a[n+1];
  for(int i=1;i<=n;i++) cin>>a[i];
  long long int dp[n+1][k+1];
  for(int i=0;i<=n;i++) dp[i][0]=1;
  for(int j=1;j<=k;j++) dp[0][j]=1;
  for(int i=1;i<=n;i++) for(int j=1;j<=k;j++) dp[i][j]=(dp[i][j-1]+dp[i-1][j]-((j>a[i])?dp[i-1][j-a[i]-1]:0))%mod;
  /*for(int i=0;i<=n;i++)
  {
      for(int j=0;j<=k;j++) cout<<dp[i][j]<<" ";
      cout<<"\n";
  }*/
  cout<<(dp[n][k]-((k>0)?dp[n][k-1]:0)+mod)%mod;
}