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) {
        Scanner scanner = new Scanner(System.in);
        int count = scanner.nextInt();
        int candies = scanner.nextInt();
        int[] arr = new int[count];
        for (int i = 0; i < count; ++i) {
            arr[i] = scanner.nextInt();
        }

        long[][] dp = new long[count + 1][candies + 1];
        dp[0][0] = 1;
        for (int i = 0; i <= count; ++i) {
            for (int j = 0; j <= candies; ++j) {
                if (i > 0) {
                    dp[i][j] = dp[i - 1][j];
                    if (j > arr[i - 1]) {
                        dp[i][j] += 1000000007 - dp[i - 1][j - arr[i - 1] - 1];
                    }
                    dp[i][j] %= 1000000007;
                }
                if (j > 0) {
                    dp[i][j] += dp[i][j - 1];
                    dp[i][j] %= 1000000007;
                }
            }
        }

        long ans = dp[count][candies];
        if (candies > 0) {
            ans += 1000000007 - dp[count][candies - 1];
        }
        System.out.println(ans % 1000000007);
    }
}
