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 {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String firstLine[] = scanner.nextLine().split(" ", 2);

        int n = Integer.parseInt(firstLine[0]);
        long m = Long.parseLong(firstLine[1]);

        long max = new Main().maxNum(n, m);
        System.out.println(max);
    }

    public long maxNum(int n, long m) {
        long max = 1;
        for (long base = 2; base <= m; base++) {
            long sum = n * base;
            if (sum <= m && (m - sum) % base == 0) {
                max = base;
            }
        }
        return max;
    }
}