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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in= new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		int arr [] = new int[n];
		int dp[] = new int[k+1];
		for( int i=0;i<n;i++) {
			arr[i] = in.nextInt();
		}
		int mod= (int)1e9 + 7;
		dp[0] =1;
		int dpPrev[] = new int[k+1];
		int sum=0;
		for(int i=1;i<=n;i++) {
			 sum+= arr[i-1];
			 Arrays.fill(dpPrev,0);
			 dpPrev[0]=1;
			 for(int j=1;j<=k;j++)
				 dpPrev[j]=(dpPrev[j-1]%mod + (int)dp[j]%mod)% mod;
			for(int j=1;j<=k; j++) {
			           if(arr[i-1]-j>=0)	
			             dp[j]= dpPrev[j]%mod;
			           else {
			        	   dp[j]=(dpPrev[j] - dpPrev[j-arr[i-1]-1] + mod)%mod;
			           }
			           
			           
			   }
		}
		
		System.out.println(dp[k]);
	}

}
