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;
using System.Text;

namespace ABC136
{
    class Program5
    {
        static void Main()
        {
            var input = Console.ReadLine().Split(' ').Select(int.Parse);
            var N = input.First();
            var K = input.Skip(1).First();
            var A = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

            var xList = new List<long>();
            long sum = A.Sum();
            var sq = (long)Math.Sqrt(sum);
            for (long i = 2; i <= sq; i++)
                if (sum % i == 0)
                    xList.Add(i);

            var len = xList.Count;
            for (int i = len - 1; i >= 0; i--)
                xList.Add(sum / xList[i]);

            xList.Add(sum);
            xList.Reverse();

            foreach (var x in xList)
            {
                var plus = 0L;
                var minus = 0L;
                for (int i = 0; i < N; i++)
                {
                    if (A[i] % x <= x / 2)
                        minus += A[i] % x;
                    else
                        plus += x - A[i] % x;
                }

                if (plus + minus <= 2 * K && Math.Abs(plus - minus) % x == 0)
                {
                    Console.WriteLine(x);
                    return;
                }
            }

            Console.WriteLine(1);
        }
    }
}