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;

/**
 * Candies
 */
public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            int N = sc.nextInt();
            int K = sc.nextInt();
            int[] A = new int[N + 1];
            for (int i = 1; i <= N; i++) {
                A[i] = sc.nextInt();
            }

            long[][] dp = new long[N + 1][K + 1];
            dp[0][0] = 1;

            for (int i = 1; i <= N; i++) {
                for (int j = 0; j <= K; j++) {
                    dp[i][j] = dp[i - 1][j];

                    if (j > 0 && A[i] > 0) {
                        dp[i][j] += dp[i][j - 1];
                        if (j - A[i] - 1 >= 0) {
                            dp[i][j] -= dp[i - 1][j - A[i] - 1];
                        }

                        dp[i][j] = (dp[i][j] + 1000000007) % 1000000007;
                    }
                }
            }

            System.out.println(dp[N][K]);
        }
    }

}
