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)

fun main(args: Array<String>) {
    val (N, M) = readInputLine().split(" ").map { it.toLong() }
    
    val divisors = mutableSetOf<Long>()
    
    for (i in 1..M) {
        if (i * i > M) {
            break
        }
        if (M % i == 0L) {
            divisors.add(i)
            divisors.add(M / i)
        }
    }
    
    var ans = 1L
    
    for (i in divisors.sorted()) {
        if (N > M / i) {
            break
        }
        
        ans = i
    }
    
    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}