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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

//package javaapplication9;
import java.util.*;
import java.io.*;
public class Main{

 public static int candies(int n, int k, int arr[],int[][] dp){
     
    if(n < 0 || k < 0)
        return 0;
     if(k == 0 && n == 0)
         return 1;
     if(dp[n][k] > 0){
//         System.out.println("used");
         return dp[n][k];
     }
     int a = 0;
     
     for(int i = 0; i <= arr[n]; i++){
      a +=candies(n-1,k-i,arr,dp);
     }
     
     return dp[n][k] =  a;
    

 
 } 
    public static void main(String[] args) throws Exception {
         BufferedReader br = new BufferedReader(new InputStreamReader(System.in));   
         StringTokenizer str  = new StringTokenizer(br.readLine()," ");
    
      int n  = Integer.parseInt(str.nextToken());
    int k  = Integer.parseInt(str.nextToken());
    int[] arr = new int[n+1];
    str  = new StringTokenizer(br.readLine()," ");
    int i = 1;
    while(str.hasMoreTokens()){
        arr[i] = Integer.parseInt(str.nextToken());
    i++;
    }
 
    int[][] dp = new int[n+1][k+1];
      System.out.println(candies(n,k,arr,dp ) );
    
    
    }
    
}