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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
import java.lang.Math.*

fun main(args: Array<String>) {
  val (n, m) = readLine()!!.split(" ").map { it.toInt() }
  var list = ArrayList<Int>()
  val sqrtM = sqrt(m.toDouble()).toInt()
  for (i in 1..sqrtM) {
    if (m % i == 0) {
      if (i <= m / n) list.add(i)
      if (i * i != m && m / i <= m / n) list.add(m / i)
    }
  }
  val ans = list.max()
  println(ans)
}