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 (2.13.1) (judge verdict: Wrong Answer)

import scala.io.StdIn.readLine

object Main extends App {
  val Array(n, m) = readLine().split(' ').map(_.toInt)
  
  import scala.math._
  
  lazy val limit: Int = {
    val a: Int = sqrt(m).ceil.toInt
    val b: Int = m / n
    if (a <= b) a else b
  }
  
  if (n == 1)
    println(m)
  else {
    val result: (Int, Boolean) = (1 to limit).map { x =>
      (x, m % x == 0)
    }
      .filter(t => t._2)
      .last
    println(result._1)
  }
}