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.util.Scanner;

public class Main{

	public static void main(String[] args) {

		Scanner scanner = new Scanner(System.in);
		String[] temp1 = scanner.nextLine().split(" ");
		int n = Integer.parseInt(temp1[0]);
		int m = Integer.parseInt(temp1[1]);

		int ans = 0;
		int temp = 0;
		//m/n
		int a1 = (int) Math.floor(m / n);

		//mの約数
		for(int i = a1; i > 1; i--) {
			temp = m;
			if(temp % i == 0) {
				ans = i;
				break;
			}
		}
		System.out.println(ans);
	}
}