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.util.Scanner;

public class Main{
	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		String inputNK = scanner.nextLine();
		String[] nkStr = inputNK.split(" ", 0);
		
		String inputP = scanner.nextLine();
		String[] pStr = inputP.split(" ", 0);
		
		int n = Integer.parseInt(nkStr[0]);
		int k = Integer.parseInt(nkStr[1]);
		
		int pInt[] = new int[n];
		for(int i=0;i<n;i++){
			pInt[i] = Integer.parseInt(pStr[i]);
		}
		
		int sum = 0;
		for(int i=0;i<n;i++){
			sum += pInt[i];
		}
		// 平均値
		int ave = sum/n;
		
		// 約数
		int divisor = ave;
		
		// 平均値または最も近い平均値の約数までいくつ差があるかの数列
		int differ[] = new int[n];
		
		divisor = ave+1;
		while(divisor > 1){
			divisor = lesserDivisor(ave, divisor);
			
			for(int i=0;i<n;i++){
				int nearest = pInt[i] - (pInt[i]%divisor);
				if(pInt[i] - nearest > divisor/2){
					nearest += divisor;
				}
				differ[i] = pInt[i] - nearest;
			}
			
			int sumOfUpperThanDiffer = 0;
			for(int i=0;i<n;i++){
				if(differ[i] > 0){
					sumOfUpperThanDiffer += differ[i];
				}
			}
			
			if(sumOfUpperThanDiffer <= k){
				break;
			}
		}
		System.out.println(divisor);
	}
	
	public static int lesserDivisor(int ave, int divisor){
		divisor--;
		while(divisor > 1){
			if(ave%divisor == 0){
				return divisor;
			}
			divisor--;
		}
		if(divisor <= 0){
			divisor = 1;
		}
		return divisor;
	}
}