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);

    long M = 1_000_000_007;
    int N = scanner.nextInt();
    int K = scanner.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++) a[i] = scanner.nextInt();

    long[][] dp = new long[N][K + 1];
    for (int i = 0; i <= a[0]; i++) dp[0][i] = 1;
    for (int i = 1; i < N; i++) {
      long sum = 0;
      for (int j = 0; j <= K; j++) {
        sum += dp[i - 1][j];
        if (sum > M) sum -= M;
        if (j > a[i]) sum -= dp[i - 1][j - a[i] - 1];
        if (sum < 0) sum += M;
        dp[i][j] = sum;
      }
    }
    System.out.println(dp[N - 1][K]);
  }
}
