Problem:
Score : 500 points

Problem Statement

We have a sequence of N integers: A_1, A_2, \cdots, A_N.

You can perform the following operation between 0 and K times (inclusive):

Choose two integers i and j such that i \neq j, each between 1 and N (inclusive). Add 1 to A_i and -1 to A_j, possibly producing a negative element.

Compute the maximum possible positive integer that divides every element of A after the operations. Here a positive integer x divides an integer y if and only if there exists an integer z such that y = xz.

Constraints

2 \leq N \leq 500

1 \leq A_i \leq 10^6

0 \leq K \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_{N-1} A_{N}

Output

Print the maximum possible positive integer that divides every element of A after the operations.

Sample Input 1

2 3
8 20

Sample Output 1

7

7 will divide every element of A if, for example, we perform the following operation:

Choose i = 2, j = 1. A becomes (7, 21).

We cannot reach the situation where 8 or greater integer divides every element of A.

Sample Input 2

2 10
3 5

Sample Output 2

8

Consider performing the following five operations:

Choose i = 2, j = 1. A becomes (2, 6).

Choose i = 2, j = 1. A becomes (1, 7).

Choose i = 2, j = 1. A becomes (0, 8).

Choose i = 2, j = 1. A becomes (-1, 9).

Choose i = 1, j = 2. A becomes (0, 8).

Then, 0 = 8 \times 0 and 8 = 8 \times 1, so 8 divides every element of A. We cannot reach the situation where 9 or greater integer divides every element of A.

Sample Input 3

4 5
10 1 2 22

Sample Output 3

7

Sample Input 4

8 7
1 7 5 6 8 2 6 5

Sample Output 4

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

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

public class Main{
	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] line = br.readLine().split(" ");
		int n = Integer.parseInt(line[0]);
		int k = Integer.parseInt(line[1]);
		line = br.readLine().split(" ");
		int[] nums = new int[n];
		int i, j, now, tmp;
		int sum = 0;
		
		for(i=0; i<n; i++){
			now = Integer.parseInt(line[i]);
			sum += now;
			for(j=0; j<i; j++) if( now < nums[j] ){
				tmp = nums[j];
				nums[j] = now;
				now = tmp;
			}
			nums[i] = now;
		}
		
		int deltaSum = 0;
		for(i=sum; 0<i; i--) if(sum/i*i == sum){
			tmp = sum/i;
			for(j=0; j<n; j++)
				deltaSum += Math.min(Math.abs(nums[j]/i*i-nums[j]), Math.abs(nums[j]/i*i+i-nums[j]));
			if( deltaSum/2 <= k ){
				System.out.println(i);
				System.exit(0);
			}
		}
	}
}