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 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Main
{
    static int dp[][];
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        String str[]=br.readLine().split(" ");
        int n=Integer.parseInt(str[0]);
        int m=Integer.parseInt(str[1]);
        String s[]=br.readLine().split(" ");
        int arr[]=new int[s.length];
        for(int i=0;i<s.length;i++)
            arr[i]=Integer.parseInt(s[i]);
        int k=Integer.parseInt(str[1]);
        dp=new int[k+1][arr.length+1];
        for(int i=0;i<dp.length;i++)
            for(int j=0;j<dp[0].length;j++)
                dp[i][j]=-1;
        System.out.println(calculate(arr,0,k));
    }

    private static int calculate(int[] arr, int index, int k) {
        if(index==arr.length-1)
        {
            if(k<=arr[index])
                return 1;
            else return 0;
        }
        if(dp[k][index]!=-1)
            return dp[k][index];
        int res=0;
        for(int i=0;i<=arr[index];i++)
        {
            res+=calculate(arr,index+1,k-i);
        }
        return dp[k][index]= res;
    }
}