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: Time Limit Exceeded)

import java.util.Scanner

object Main {
  def main(args: Array[String]) {
    val result = solve(new Scanner(System.in))
    if (result.length > 0) println(result)
  }

  def solve(in: String): String = solve(new Scanner(in))

  def solve(sc: Scanner): String = {
    val N = sc.nextInt
    val M = sc.nextInt

    var n = N
    while (n <= M && M % n != 0) {
      n += 1
    }
    if (n > M) "1" else (M / n).toString
  }
}