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"
	"os"
	"strconv"
	"fmt"
)

var sc = bufio.NewScanner(os.Stdin)

func nextString() string {
	if !sc.Scan() {
		panic("failed scan string")
	}
	return sc.Text()
}

func nextInt() int {
	if !sc.Scan() {
		panic("failed scan int")
	}
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func main() {
	sc.Split(bufio.ScanWords)

	n := nextInt()
	m := nextInt()

	if m > 10000 {
		var result int

		for i := 1; i <= 100; i ++ {
			if m%i == 0 {
				result = i
			}
		}

		for ; n <= m/99; n++ {
			if m%n == 0 {
				fmt.Println(m / n)
				return
			}
		}
		fmt.Println(result)
		return
	} else {
		for ; n <= m; n++ {
			if m%n == 0 {
				fmt.Println(m / n)
				return
			}
		}
	}

}