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.*;

public class Main {
	Scanner sc = new Scanner(System.in);
	static boolean prime[];
	void doIt() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		System.out.println(getGcd(n, m));
	}

	int getGcd(int n, int m) {
		int num = 1;
		for(int i = m / n; i >= 1; i--) {
			if(m % i == 0) {
				if(m / i >= n) {
					return i;
				}
			}
		}
		return num;
	}
	Main(){doIt();}
	public static void main(String[] args) {
		new Main();
	}

}