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)

//package abc136;

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

public class Main {

	/**
	 * @param args
	 * @throws IOException 
	 */
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String[] tmpArray = br.readLine().split(" ");
		int n = Integer.parseInt(tmpArray[0]);
		int k = Integer.parseInt(tmpArray[1]);
		
		int input[] = new int[n];
		
		tmpArray = br.readLine().split(" ");
		
		long sum = 0;
		for(int i = 0; i < n; i++){
			input[i] = Integer.parseInt(tmpArray[i]);
			sum += input[i];
		}
		
		long divisor = 1;
		long result = 1;
		while(sum/divisor > 1){
			long tmpGCD = sum/divisor;
			
			long plus = 0;
			long minus = 0;
			for(int i = 0; i < n; i++){
				long tmpPlus = tmpGCD - (input[i]%tmpGCD);
				long tmpMinus = input[i]%tmpGCD;
				if(tmpPlus <= tmpMinus){
					plus += tmpPlus;
				}
				else {
					minus += tmpMinus;
				}
			}
			
//			System.out.println("plus "+plus+" minus "+ minus);
			if(minus <= k){
				result = tmpGCD;
				break;
			}
//			System.out.println((sum/divisor) + "is failed");
			
			for(long i = divisor + 1; i <= sum; i++){
				if(sum % i == 0){
					divisor = i;
					break;
				}
			}
			
			
		}
		
		System.out.println(result);
	}

}