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.io.*;
import java.util.*;

@SuppressWarnings("unchecked")
public class Main {
    private static final long MOD = (int)1e9 + 7;

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) a[i] = in.nextInt();

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

        for (int i = 0; i <= a[0]; ++i) dp[0][i] = 1;

        pre[0][0] = dp[0][0];
        for (int i = 1; i <= k; ++i) pre[0][i] = (pre[0][i - 1] + dp[0][i]) % MOD;

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

            pre[i][0] = dp[i][0] % MOD;
            for (int x = 1; x <= k; ++x) {
                pre[i][x] = (pre[i][x - 1] + dp[i][x]) % MOD;
            }
        }

        System.out.println(dp[n - 1][k] % MOD);
    }
}