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: Accepted)

object Main{
  def main(args:Array[String]):Unit={
    var nm = readLine.split(" ").map(x => x.toInt)  
    var n = nm(0)
    var m = nm(1)
    var max = m/n
    var flag = true
    for(i <- max until 0 by -1 if flag){
      if(m%i==0){
        println(i)
        flag = false
      }
    }
  }
}