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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

    private static List<Long> divisor(long n) {
        List<Long> list = new ArrayList<>();
        for (long i = 1; i * i <= n; i++) {
            if (n % i == 0) {
                list.add(i);
                long j = n / i;
                if (j != i) {
                    list.add(j);
                }
            }
        }
        Collections.sort(list);
        return list;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long m = sc.nextLong();
        List<Long> div = divisor(m);
        long ans = 1;
        for (int i = 0; i < div.size(); i++) {
            long d = div.get(i);
            if (d * n <= m) {
                ans = Math.max(ans, d);
            }
        }
        System.out.println(ans);
    }

}