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
{
    private final static int MOD = 1_000_000_007;
 
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
	String[] temp = in.nextLine().split(" ");
	int N = Integer.parseInt(temp[0]);
	int K = Integer.parseInt(temp[1]);
	int[] arr = new int[N];
	temp = in.nextLine().split(" ");
	for (int i = 0; i < N; i++) {
	    arr[i] = Integer.parseInt(temp[i]);
	}
	long[][] dp = new long[N+1][K+1];
	dp[0][0] = 1;
	for (int i = 1; i <= N; i++) {
	    dp[i][0] = 1;
	    for (int j = 0; j < K; j++) {
		dp[i][j+1] = dp[i][j] + dp[i-1][j+1];
		dp[i][j+1] %= MOD;
		if (j - arr[i-1] >= 0) {
		    dp[i][j+1] = dp[i][j+1]-dp[i-1][j-arr[i-1]] + MOD;
		    dp[i][j+1] %= MOD;
		}
	    }
	}
	System.out.println(dp[N][K] % MOD);
	in.close();
    }
}
