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.*;

public class Main
{
    public static void main(String []args)
    {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        
        int arr[] = new int[n];
        for(int i = 0 ; i< n ; i++)
        {
            arr[i] = sc.nextInt();
        }
        long mod = 1000000007;
        long dp[][] = new long[n+1][k+1];
        for(int i = 0 ; i <= k ; i++)
        {
            dp[0][i] = 1;
        }
        
        for(int i = 1 ; i <= n ; i++)
        {
            for(int kk = 0 ; kk <= k ; kk++)
            {
                if(arr[i-1] >= kk)
                dp[i][kk] += dp[i-1][kk];
                
                else
                dp[i][kk] += dp[i-1][kk] - dp[i-1][kk-arr[i-1]-1];
                
                dp[i][kk] %= mod;
            }
            
            for(int kk = 1 ; kk <= k ; kk++)
            {
                dp[i][kk] += dp[i][kk-1];
                dp[i][kk] %= mod;
            }
        }
        if(k > 0)
        System.out.println((dp[n][k] - dp[n][k-1]+mod)%mod);
        
        else
        System.out.println(dp[n][k]);
    }
}