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 <iostream>
#include <vector>

using namespace std;
typedef long long ll;

int main()
{
  int N, K;
  cin >> N >> K;
  vector<int> a(N);
  for( int i=0;i<N; ++i )
    cin >> a[i];
  vector< vector<ll> > dp(N+1, vector<ll>(K+1));

  dp[0][0] = 1;
  for( int i=0;i<N; ++i )
    {
      int cumsum = 0;
      for( int j=0;j<K+1;++j )
	{
	  cumsum = (cumsum+dp[i][j])%1000000007;
	  dp[i+1][j] = cumsum;
	  if( j>a[i]-1 )
	    cumsum = (1000000007+cumsum-dp[i][j-a[i]])%1000000007;
	}
    }
  cout << dp[N][K] << endl;
  
}
