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.Text;
using System.Linq;

namespace codeTester.contest190804
{
    class ProblemE
    {
        static List<long> nk = new List<long>();
        static List<long> aList = new List<long>();
        static long answer = 0;

        public static void Main(string[] args)
        {
            Input();
            Logic();
            Output();
        }

        static void Input()
        {
            nk = ReadSpaceSeparatedValues();
            aList = ReadSpaceSeparatedValues();
        }

        public static List<long> ReadSpaceSeparatedValues()
        {
            List<long> values = new List<long>();
            string[] inputs = Console.ReadLine().Split(' ');
            foreach (string input in inputs)
            {
                values.Add(long.Parse(input));
            }

            return values;
        }

        public static void Logic()
        {
            // とりあえず入力値の約数を全部探す。
            int n = (int) nk[0];
            long k = nk[1];
            long aSum = aList.Sum();
            long sqrtA = (long) Math.Floor(Math.Sqrt(aSum));
            List<long> divisors = new List<long>();

            for (long i = 1; i <= sqrtA; i++)
            {
                if (aSum % i == 0)
                {
                    divisors.Add(i);
                    divisors.Add(aSum / i);
                }
            }

            List<long> sortedDivisors = divisors.OrderByDescending(v => v).ToList();
            DebugPrint("DIVS : " + string.Join(" ", sortedDivisors));

            // 最も大きい公約数から順に狙っていく
            foreach (long v in sortedDivisors)
            {
                DebugPrint(v.ToString());
                // 過不足の調整に必要な処理回数を計算する。
                long needOperationTime = aList.Aggregate((long) 0, (ttl, a) =>
                {
                    return ttl + Math.Min((a + v) % v, v - ((a + v) % v));
                });
                if (needOperationTime <= k * 2)
                {
                    answer = v;
                    return;
                }
            }
        }

        static void Output()
        {
            Console.WriteLine(answer.ToString());
        }

        static void DebugPrint(string msg)
        {
            // 提出時に消す
            // Console.WriteLine(msg);
        }
    }
}