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 in=new Scanner(System.in);
		int n=in.nextInt();
		int K=in.nextInt();
		int mod=1000000007;
		int[] dp=new int[K+1];
		int[] a=new int[n+1];
		for (int i=1;i<=n;++i)
			a[i]=in.nextInt();
		dp[0]=1;
		for (int i=1;i<=n;++i) {
			for (int j=1;j<=K;++j)
				dp[j]=(dp[j]+dp[j-1])%mod;
			for (int j=K;j>=0;--j)
				dp[j]=(dp[j]-((j<a[i]+1)?0:dp[j-a[i]-1]))%mod;
		}
		System.out.println((dp[K]+mod)%mod);
	}
}