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.*;

public class Main {

    static ArrayList<Integer> divisor(int x) {
        ArrayList<Integer> ans = new ArrayList<Integer>();
        for (int i=1;i*i<=x;i++) {
            if (x%i==0) ans.add(i);
            if (x%i==0 && i*i!=x) ans.add(x/i);
        }
        Collections.sort(ans);
        return ans;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int K = Integer.parseInt(sc.next());
        int[] A = new int[N];
        int sum = 0;
        for (int i=0;i<N;i++) {
            A[i] = Integer.parseInt(sc.next());
            sum += A[i];
        }
        ArrayList<Integer> list = divisor(sum);
        for (int i=list.size()-1;i>=0;i--) {
            int tmp = list.get(i);
            int[] B = new int[N];
            for (int j=0;j<N;j++) {
                B[j] = A[j]%tmp;
            }
            Arrays.sort(B);
            int right = N-1;
            long cnt = 0L;
            for (int j=0;j<N;j++) {
                if (j>right) break;
                int val = B[j];
                cnt += val;
                // System.out.println(tmp+" "+Arrays.toString(B));
                while (val>0) {
                    if (j==right) break;
                    if (tmp-B[right]>val) {
                        B[right]+=val;
                        val-=val;
                    } else { //  tmp-B[right]<=val
                        B[right]+=tmp-B[right];
                        val-=tmp-B[right];
                        right--;
                    }
                }
            }
            if (cnt<=K) {
                System.out.println(tmp);
                return;
            }
        }
    }
}