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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

var s = bufio.NewScanner(os.Stdin)

func next() int64 {
	s.Scan()
	i, _ := strconv.ParseInt(s.Text(), 10, 64)
	return i
}

func main() {
	s.Split(bufio.ScanWords)
	N := next()
	M := next()

	d := int64(math.Floor(math.Sqrt(float64(M))))

	for ; d >= 1; d-- {
		if M%d != 0 {
			continue
		}

		p := M / d
		if p >= N {
			fmt.Println(d)
			return
		}
	}
}