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 Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func main() {
	var n, m int
	fmt.Scan(&n, &m)

	if n == 1 {
		fmt.Println(m)
		return
	}

	ans := 1
	for i := 2; i*i <= m; i++ {
		if m%i != 0 {
			continue
		}
		if i*n <= m && i > ans {
			ans = i
		}
		if j := m / i; j*n <= m && j > ans {
			ans = j
		}
	}
	fmt.Println(ans)
}