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;
import java.util.Arrays;

public class Main {
	static int[][] cache;
	static final int MOD = 1000000007;
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] S = br.readLine().split(" ");
		int N = Integer.parseInt(S[0]);
		int K = Integer.parseInt(S[1]);
		
		int[] A = new int[N];
		
		S = br.readLine().split(" ");
		for(int i = 0; i < N ; i++) {
			A[i] = Integer.parseInt(S[i]);
		}
		
		cache = new int[N][K+1];
		
		for(int i = 0; i < N; i++) {
			cache[i][0]  = 1;
		}
		
		int temp =  Math.min(K, A[0]);
		for(int i = 1 ; i <= temp; i++) {
			cache[0][i] = 1;
		}
		
		System.out.println(ways(A, K));
	}
	
	public static int ways(int[] A, int K) {
		int N = A.length;
		
		for(int i = 1; i < N ; i++) {
			for(int k = 1; k <= K; k++) {
				int result = 0;
				int temp =  Math.min(k, A[i]);
				
				for(int j = 0; j <= temp; j++) {
					result = (result + cache[i-1][k-j]) % MOD;
				}
				cache[i][k] = result;
			}
		}
		
		return cache[N-1][K];
	}
}