Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3 4
1 2 3

Sample Output 1

5

There are five ways for the children to share candies, as follows:

(0, 1, 3)

(0, 2, 2)

(1, 0, 3)

(1, 1, 2)

(1, 2, 1)

Here, in each sequence, the i-th element represents the number of candies that Child i receives.

Sample Input 2

1 10
9

Sample Output 2

0

There may be no ways for the children to share candies.

Sample Input 3

2 0
0 0

Sample Output 3

1

There is one way for the children to share candies, as follows:

(0, 0)

Sample Input 4

4 100000
100000 100000 100000 100000

Sample Output 4

665683269

Be sure to print the answer modulo 10^9 + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

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;
    for (int i = 1; i <= N; i++) {
      for (int j = 0; j <= K; j++) {
        int cur = 0;
        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;
      }
    }
    

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

}