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: Time Limit Exceeded)

// Package main provides
//
// File:  d.go
// Author: ymiyamoto
//
// Created on Sat Dec  1 14:35:30 2018
//
package main

import "fmt"

var n, m int

func gcd(a, b int) int {
	if a%b == 0 {
		return b
	}
	return gcd(b, a%b)
}

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

	maxGCD := 1
	for i := 2; i <= m; i++ {
		min := i
		max := m - (n-1)*min

		if max <= 0 || min > max {
			break
		}

		g := gcd(min, max)
		if maxGCD < g {
			maxGCD = g
		}
	}

	fmt.Println(maxGCD)
}