Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Scala (2.11.7) (judge verdict: Runtime Error)

import java.util.Scanner

import scala.collection.mutable

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val xyhs = Seq.fill(n)((sc.nextInt, sc.nextInt, sc.nextInt))
  val excludes = xyhs.map { case (x, y, _) => (x, y) }
  val h_xys = mutable.Map.empty[(Int, Int), Int]
  xyhs.foreach { case (x, y, h) =>
    for {
      xx <- 0 to 100
      yy <- 0 to 100
    } {
      val hh = Math.abs(x - xx) + Math.abs(y - yy) + h
      val already = h_xys.get((xx, yy))
      if ((x, y) != (xx, yy) && excludes.contains((xx, yy))) {
        
      } else if (already.isEmpty) {
        h_xys.update((xx, yy), hh)
      } else if (already.exists(_ != hh)) {
        h_xys.update((xx, yy), -1)
      }
    }
  }
  val center = h_xys.maxBy { case (_, h) => h }
  println(s"${center._1._1} ${center._1._2} ${center._2}")
}