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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
list($n, $k) = ints();
$aArray = ints();
$sum = array_sum($aArray);
$d = divisor($sum);
$d = array_reverse($d);
foreach($d as $dd){
  $modArray = [];
  foreach($aArray as $a){
    $modArray[] = $a%$dd; 
  }
  sort($modArray);
  $end = $n;
  $tmp = 0;$sum = 0;
//  o($modArray);
  for($i = 0; $i < $end; $i++){
    $tmp += $modArray[$i];
    $sum += $modArray[$i];
    while($tmp > 0){
      $tmp-=$dd - $modArray[$end - 1];
      $end--;
    }
  }
//  o($sum, $tmp);
  if($sum <= $k && $tmp == 0){
    echo $dd;
    exit;
  }
}

function divisor($n){
    for($i = ceil(sqrt($n)); $i >= 1; $i--){
        if($n % $i == 0){
            $f[] = $i;
            $f[] = $n / $i;
        }
    }
    sort($f);
    return array_unique($f);
}

function str(){
  return trim(fgets(STDIN));
}
function ints(){
  return array_map("intval", explode(" ", trim(fgets(STDIN))));
}
function int(){
  return intval(trim(fgets(STDIN)));
}
function o(...$val){
    if(count($val)==1)$val = array_shift($val);
    $trace = debug_backtrace();
    echo $trace[0]['line'].")";
    if(is_array($val)){
        if(count($val) == 0){
            echo "empty array";
        }elseif(!is_array(current($val))){
            echo "array:";
            echo implode(" ", $val)."\n";
        }else{
            echo "array:array\n";
            foreach($val as $row){
                echo implode(" ", $row)."\n";
            }
        }
    }else{
        echo $val."\n";
    }
}