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.*

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