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"
	"math"
	"sort"
)

func main() {
	var n,m int
	fmt.Scan(&n,&m)
	
	limit := int(math.Floor(math.Sqrt(float64(m))))
	div := []int{}
	for i:=1; i <= limit; i++ {
		if m % i ==0{
			div = append(div,i)
			div = append(div,m/i)
		}
	}

	sort.Sort(sort.IntSlice(div))
	for i := len(div)-1; i >= 0; i -= 1{
		if m/div[i] >= n {
			fmt.Println(div[i])
			return
		}
	}
}