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


//12;03
import java.util.Scanner;

public class Main {

	private static Scanner in;
	private static int n;
	private static int[] a;
	private static int k;
	private static int[] dp;
	private static final int MOD = (int)1e9+7;
	
	public static void main(String[] args) {
		in = new Scanner(System.in);
		n = in.nextInt();
		k = in.nextInt();
		a = new int[n];
		for(int i=0; i<n; i++) a[i] = in.nextInt();
		dp = new int[k+1];
		dp[0] = 1;
		
		for(int i=n-1; i>=0; i--) {
			int[] pre = new int[k+1];
			pre[0] = dp[0];
			for(int j=1; j<k+1; j++) {
				pre[j] = (pre[j-1]+dp[j])%MOD;
			}
			
			for(int kLeft=k; kLeft>=0; kLeft--) {
				// dp[kLeft] is the sum of dp[kLeft] to dp[kLeft-a[i]]
				dp[kLeft] = ((pre[kLeft]-(kLeft-a[i]-1>=0?pre[kLeft-a[i]-1]:0))%MOD+MOD)%MOD;
			}
		}
		System.out.println(dp[k]);
		
	}

}
