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: Accepted)

import java.util.*;

public class Main {


    public static void main(String[] args){

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] a = new int[n];
        int sum = 0;
        for(int i=0; i<n; i++) {
            a[i] = sc.nextInt();
            sum += a[i];
        }
        A: for(int i = 1; i <= sum / 2; i++) {
            if(sum % i != 0) continue;
            int div = sum / i;

            int minus = 0;
            int plus = 0;

            int[] b = new int[n];


            for(int j = 0; j<n; j++) {
                b[j] = a[j] % div;
            }
            Arrays.sort(b);
            int l = 0;
            int r = n - 1;
            while(l <= r) {
                if (minus < plus) {
                    minus += b[l];
                    if(minus > k) continue A;
                    l++;
                } else {
                    plus += div - b[r];
                    if(plus > k) continue A;
                    r--;
                }
            }
            System.out.println(div);
            return;
        }

        System.out.println(1);
    }

}