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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

import static java.lang.System.in;

public class Main {
    final static long MOD = (int) (10E8 +7);
    public static void main(String[] args) {
        Scanner scanner = new Scanner(in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = scanner.nextInt();
        }
        if(k==0) {
            System.out.println(1);
            return;
        }
        long[][] dp = new long[n+1][k+1]; // children and  candies
        for(int child =0;child<=n;child++){
            for (int candy = 0; candy <= k; candy++) {
                if(candy==0 || child==0){
                    dp[child][candy]=1;
                }
                else {
                    int R = candy;
                    int L = candy - Math.min(candy, arr[child - 1]) - 1;
                    if (L == -1)
                        dp[child][candy] = (dp[child][candy]% MOD +dp[child - 1][R]% MOD) % MOD;
                    else
                        dp[child][candy] = (dp[child][candy]% MOD +dp[child - 1][R]% MOD - dp[child - 1][L]%MOD + MOD) % MOD;
                    dp[child][candy] = (dp[child][candy]% MOD+dp[child][candy - 1]% MOD) % MOD;
                }
            }
        }
        System.out.println((dp[n][k]% MOD-dp[n][k-1]% MOD + MOD)% MOD);
    }
}