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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
 {
        static void Main(string[] args)
        {
        　　int n, k;
            string[] NK = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
            n = int.Parse(NK[0]); //標準入力
            k = int.Parse(NK[1]); //標準入力
            string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
            int[] a = str.Select(x => int.Parse(x)).ToArray();

            int sum = a.Sum();
            var list = new List<int>();
            for(int i=1;i*i<=sum;++i)
            {
                if (sum % i == 0)
                {
                    list.Add(i);
                    list.Add(sum / i);
                }
            }
            var ans = 1;
            foreach(var i in list)
            {
                int need = 0;
                need = CalcX(i, a, k);
                if( need <= k) { ans = Math.Max(ans, i); }
            }

            Console.WriteLine(ans);
        }

        /// <summary>
        ///
        /// </summary>
        /// <param name="x">約数x</param>
        /// <returns></returns>
        private static int CalcX(int x, int[] a, int k)
        {
            var b = new List<int>(a);
            for(int i=0;i<b.Count;++i)
            {
                b[i] %= x;
            }
            b.Sort();

            int tot = b.Sum();
            int l = b.Count - tot / x;
            int need = 0;
            for(int i=0;i<l;++i)
            {
                need += b[i];
            }
            return need;
        }
 }