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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

public class S
{



    public static void Main()
	{
		/*
        var input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        var N = input[0];
        var M = input[1];
        var bridge = new int[M,2];
        for(int i = 0; i < M; i++){
            input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            bridge[i,0] = input[0];
            bridge[i,1] = input[1];
        }
        solver(N,M,bridge);
		*/
		var input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
        var N = int.Parse(input[0].ToString());
        var M = input[1];
		solver(N,M,Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse));
        //solver(2, 10, new int[]{3,5});
    }

    public static void solver(int N, int K, int[] input){

        var sum = input.Sum();

        var divisors = getDivisorList(sum);
        Array.Sort(divisors);
        var amari = new int[input.Length];

        // amari list

        int max = input.Max();
        int amariTot = 0;
        int moveCount = 0;

        for(int i = divisors.Length-1; i >=0 ; i--){

            amariTot = 0;
            moveCount = 0;
            for(int k = 0; k < input.Length; k++){
				//Console.WriteLine(k);
                amari[k] = input[k] % divisors[i];
                amariTot += input[k] % divisors[i];

            }

            Array.Sort(amari);
            amari.Reverse();
            amariTot /= divisors[i];

            for(int k = 0; k < amariTot; k++){
                
                moveCount += Math.Abs(divisors[i] - amari[k]);

                
                
            }
			
            if(moveCount <= K){
                Console.WriteLine(divisors[i]);
                return;
            }
			
			

        }



    }


    public static int[] getDivisorList(int num){
        int x = 1;

        int cap = Convert.ToInt32(Math.Sqrt(num));


        var result = new List<int>();
        while(x <= cap){
            if(num % x == 0){
                if(x == num /x){
                    result.Add(x);
                }else{
                    result.Add(x);
                    result.Add(num/x);
                }
            } 
            x++;
        }
		return result.ToArray();
    }

}