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 scanner = Scanner(System.`in`)
	val n = scanner.nextLong()
	val m = scanner.nextLong()
	println(calc(n, m))
}

fun calc(n: Long, m: Long): Long {
	for (i in m / n downTo 1) {
		if (m % i == 0L && m / n >= i) return i
	}
	return 1
}