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: Time Limit Exceeded)



import java.util.Scanner;

public class Main {

    static Scanner sc = new Scanner(System.in);


    static long n;
    static long m;


    public static void main(String[] args) {
        n = sc.nextLong();
        m = sc.nextLong();

        long result = solve(n, m);
        System.out.println(result);
    }

    private static long solve(long n, long m) {
        long ans = 0;
        long num = 1;
        while (num <= m / n) {
            if (m % num == 0) {
                if (m / num >= n) {
                    ans = num;
                }
            }
            num++;
        }
        return ans;
    }
}