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.Scanner;
import java.util.Vector;

public class Main {
	static long dp[][];
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		dp = new long [n][k+1];
		for (int i=0;i<n;i++) {
			int a=sc.nextInt();
			for (int j=0;j<=k;j++) {
				dp[i][j] = 0;
				if (i==0) {
					if (a>=j) dp[i][j] = 1;
				} else {
					if (j==0) dp[i][j] = 1;
					else {
						dp[i][j] = (dp[i][j-1] + dp[i-1][j])%1000000007;
						if (j>=a+1) dp[i][j] = (dp[i][j]+ 1000000007  - dp[i-1][j-a-1])%1000000007;
					}
				}
			}
		}
		System.out.println(dp[n-1][k]);
	}
}
