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;

public class Main {
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){

			long mod = (long)1e9+7;
			int N = scan.nextInt();
			int K = scan.nextInt();
			int[]a = new int[N+1];
			for(int i = 1;i<=N;i++)a[i] = scan.nextInt();

			long[][]dp = new long[N+1][K+1];


			dp[0][0] =1;

			for(int i = 1;i<=N;i++) {
				long []s = new long [K+2];
				for(int j = 1;j<=K+1;j++) s[j] = (s[j-1]+dp[i-1][j-1])%mod;

				for(int j = 0;j<=K;j++){
					dp[i][j] = (s[j+1]-s[Math.max(0, j-a[i])]+mod)%mod;
				}
			}


			System.out.println(dp[N][K]);




		}


	}


}
