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.*;

public class Main {

	public static void main(String[] args) {
		Main ans = new Main();
		System.out.println(ans.solve());
	}

	private long solve() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int K = sc.nextInt();
		int MOD = (int) 1e9+7;
		int [] array = new int[N+1];
		for(int i=1;i<=N;i++) {
			array[i] = sc.nextInt();
		}

		long[][] dp = new long[N+2][K+2];

		for(int i=0;i<=K;i++) {
			dp[1][i] = (i<=array[1]) ? 1 : 0;
		}


		for(int i=2;i<=N;i++){
			for(int j=0;j<=K;j++) {
				if (j==0) dp[i][j] = dp[i-1][j];
				else {
					long val = (j-1-array[i]) >= 0 ? dp[i-1][j-1-array[i]] : 0;		
					dp[i][j] = (MOD+ dp[i-1][j] + dp[i][j-1] - val)%MOD;	
				}				
			}
		}

		return dp[N][K];

	}

}