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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int N = sc.nextInt();
		int M = sc.nextInt();
		ArrayList <Integer> yakusuuList = Main.yakusuu(M);
    
		int D = 1;

		for(int i = 0; i < yakusuuList.size(); i++){
			int an = M - (N-1)*yakusuuList.get(i);
			if(an <= 0){
				break;
			}
			if(an % yakusuuList.get(i) == 0){
				D = yakusuuList.get(i);
			}
		}
		System.out.println(D);
	}


	public static ArrayList <Integer>  yakusuu(int M) {
		ArrayList <Integer> yakusuuList = new ArrayList <Integer> ();
		for(int i=1; i<=M/2; i++){
			if(M % i == 0){
				yakusuuList.add(i);
			}
		}
		
		for(int i=yakusuuList.size()-1; i == 0; i--){
			int addNumber = M / yakusuuList.get(i);
			yakusuuList.add(addNumber);
		}
		return yakusuuList;
	}
}