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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N, K = in.next().toInt
  val A = new Array[Int](N+1)
  for (i <- 1 to N) {
    A(i) = in.next().toInt
  }

  //
  val S = A.sum
  var B = new Array[Int](N+1)

  var ans = 1L
  var n = 1
  while (n * n <= S) {
    if (S % n == 0) {
      for (i <- 1 to N) {
        B(i) = A(i) % n
      }
      B = B.sorted

      var fu = 0L
      var sei = 0L
      var l = 1
      var r = N
      while (l <= r) {
        if (fu > sei) {
          fu += B(l)
          l += 1
        }
        else {
          sei += n - B(r)
          r -= 1
        }
      }

      if (fu == sei && sei <= K)
        ans = ans max n
    }

    val m = S / n
    if (S % m == 0) {
      for (i <- 1 to N) {
        B(i) = A(i) % m
      }
      B = B.sorted

      var fu = 0L
      var sei = 0L
      var l = 1
      var r = N
      while (l <= r) {
        if (fu < sei) {
          fu += B(l)
          l += 1
        }
        else {
          sei += m - B(r)
          r -= 1
        }
      }

      if (fu == sei && sei <= K)
        ans = ans max m
    }


    n += 1
  }

  println(ans)
}

object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.deep))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}