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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int k=scan.nextInt();
		int ar[]=new int[n];
		long sum=0;
		for(int i=0;i<n;i++)
		{
			ar[i]=scan.nextInt();
			sum+=ar[i];
		}
		ArrayList<Integer> div=new ArrayList<Integer>();
		for(int i=1;i*i<=sum;i++)
		{
			if(sum%i==0)
			{
				div.add(i);
				div.add((int)(sum/i));
				
			}
			
		}
		int ans=1;
		for(int x:div)
		{
			int r[]=new int[n];
			for(int i=0;i<n;i++)
			{
				r[i]=ar[i]%x;
			}
			Arrays.sort(r);
			int inc[]=new int[n+1];
			int dec[]=new int[n+1];
			for(int j=0;j<n;j++)
			{
				dec[j+1]=dec[j]+r[j];
				inc[j+1]=inc[j]+(x-r[j]);
				
			}
//			if(x==7) {
//				for(int q:r)System.out.print(q+" ");
//				System.out.println();
////				for(int w:dec)
//				for(int q:dec)System.out.print(q+" ");
//				System.out.println();
//				for(int q:inc)System.out.print(q+" ");
//				System.out.println("new");
//				}
			for(int j=0;j<=n;j++)
			{
				if(dec[j]-dec[0]==inc[n]-inc[j])
				{
					if(dec[j]-dec[0]<=k)
					{
						ans=Math.max(ans,x);
						break;
					}
				}
			}
			
						
			
		}
		System.out.println(ans);
	}
}