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.math.*;
import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int K = sc.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++)
      a[i] = sc.nextInt();
    sc.close();

    int mod = 1000000007;

    int[][] dp = new int[N + 1][K + 1];
    dp[0][0] = 1;
    int[] cusum = new int[dp[0].length + 1];

    for (int i = 1; i < N + 1; i++) {
      for (int j = 1; j < cusum.length; j++)
        cusum[j] = (cusum[j - 1] + dp[i - 1][j - 1]) % mod;
      for (int j = 0; j < K + 1; j++)
        dp[i][j] = (cusum[j + 1] - cusum[Math.max(0,  j - a[i - 1])] + mod) % mod;
    }

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