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.*;
import java.io.*;

class Main {

  

  public static void main(String[] args) {
    Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    int INF = (int) 1e9 + 7;

    int N = in.nextInt();
    int K = in.nextInt();
    int[] a = new int[N];
    for (int i = 0; i < N; i++) {
      a[i] = in.nextInt();
    }

    int[][] dp = new int[N + 1][K + 1];
    dp[0][0] = 1;
    Arrays.fill(dp[0], 1);
    for (int i = 1; i <= N; i++) {
      for (int j = 0; j <= K; j++) {
        // int cur = 0;

        // pre + (j - a[i - 1] ... j)
        int pre = (dp[i - 1][j] - (j - a[i - 1] <= 0 ? 0 : dp[i - 1][j - a[i - 1] - 1]));
        if (pre < 0) {pre += INF;}
        dp[i][j] = (j == 0 ? 0 : dp[i][j - 1]) + pre;
        if (dp[i][j] >= INF) {dp[i][j] -= INF;}
        // for (int take = Math.min(a[i - 1], j); take >= 0; take--) {
        //   cur += dp[i - 1][j - take];
        //   if (cur > INF) {cur -= INF;}
        // }
        // dp[i][j] = cur;
      }
    }
    
    int res = dp[N][K] - (K == 0 ? 0 : dp[N][K - 1]);
    System.out.println(res < 0 ? res + INF : res);
  }

}
