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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
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];
		}
		if(sum<=K) {
			System.out.println(sum);
			return;
		}
		//System.out.println(sum);
		ArrayList<Integer> youso=new ArrayList<Integer>();
		for(int i=2;i<=(int)Math.sqrt(sum);i++) {
			if(sum%i==0) {
				i=sum/i;
				int sum2=0;
				int sum1=0;
				int b[]=new int[N];
				for(int x=0;x<N;x++) {
					b[x]=a[x]%i;

				}
				Arrays.sort(b);
				for(int x=0;x<N;x++) {
					if(sum2+b[x]<=K) {
						sum2+=b[x];
					}else {
						sum1+=i-b[x];
					}
				}

				//System.out.println(i+" "+sum2);
				if(sum2>=sum1) {
					System.out.println(i);
					return;
				}
				i=sum/i;
			}
		}
		for(int i=(int)Math.sqrt(sum);i>0;i--) {
			if(sum%i==0) {
				//int b[]=new int[N];
				int sum2=0;
				int sum1=0;
				int b[]=new int[N];
				for(int x=0;x<N;x++) {
					b[x]=a[x]%i;

				}
				Arrays.sort(b);
				for(int x=0;x<N;x++) {
					if(sum2+b[x]<=K) {
						sum2+=b[x];
					}else {
						sum1+=i-b[x];
					}
				}
				//System.out.println(i+" "+sum2);
				if(sum2>=sum1) {
					System.out.println(i);
					return;
				}

			}
		}

	}
}