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.Arrays;
import java.util.Scanner;

public class Main {

	private static Scanner in;

    private static int n, k;
    private static int[] a;
    private static long[][] dp;
    private static int MOD = (int)1e9+7;

    public static void main(String[] args) {
        in = new Scanner(System.in);
        n = in.nextInt();
        k = in.nextInt();
        a = new int[n];
        for(int i=0; i<n; i++) a[i] = in.nextInt();

        dp = new long[n+1][k+1];

        dp[n][0] = 1; //dp[n][kLeft] = 0 for all other kLeft

        long[] pre = new long[k+1];
        Arrays.fill(pre, 1);

        for(int i=n-1; i>=0; i--) {
            for(int kLeft=0; kLeft<=k; kLeft++) {
                dp[i][kLeft] += (pre[kLeft]-(kLeft-a[i]-1>=0?pre[kLeft-a[i]-1]:0)+MOD)%MOD;
            }

            pre[0] = dp[i][0];

            for(int j=1; j<pre.length; j++) {
                pre[j] = (pre[j-1]+dp[i][j])%MOD;
            }
        }

        System.out.println(dp[0][k]);


    }
    
    
}
