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