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: Wrong Answer)

import java.lang.reflect.Array;
import java.util.*;

/**
 * Created by Santa.
 */
public class Main {

    static int N;
    static int K;
    static int Q;
    static int A;
    static long B;
    static long C;
    //    static int[][] map;
    static int min = 9999999;
    static long ans = 0;


    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int N = scanner.nextInt();

        int M = scanner.nextInt();

        int l = 0;
        int r = 1000000;
        int mid;

        int ans = 1;

        for (int i = 1; i <= 100000; i++) {
            long nokori = M - (long)N * i;

            if(nokori >= 0 && nokori % i == 0)ans = i;


        }

        System.out.println(ans);



    }
}