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

import java.util.*;


public class Main{ 


    public static void main(String args[]) {
    Scanner s=new Scanner(System.in);
	int n=s.nextInt();
	int k=s.nextInt();
	int arr[]=new int[n+1];
	
	for(int i=1;i<=n;i++) {
		arr[i]=s.nextInt();
	}
	
	long dp[][]=new long[n+1][k+1];
	int mod=1000000007;
	
	//aapke paas j candies hai and i persons hai
	
	for(int j=0;j<=k;j++) {
		if(j<=arr[1])
		dp[1][j]=1;
		else
		dp[1][j]=0;
	}
	
	for(int i=2;i<=n;i++) {
		for(int j=0;j<=k;j++) {
			if(j==0)
				dp[i][j]=dp[i-1][j];
			else
				dp[i][j]=(mod+dp[i][j-1]+dp[i-1][j]- ((j-1-arr[i]>=0)?dp[i-1][j-1-arr[i]]:0)) % mod;
		}
	}
	
	
	System.out.println(dp[n][k]);
   }
}