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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	static Scanner scanner;

	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    long N=gl();
	    long M=gl();
        List<Long> l=new ArrayList<Long>();

	    for(long i=1; i<=Math.sqrt(M);i++) {
	    	if(M%i==0) {
	    		l.add(i);
	    		l.add(M/i);
	    	}
	    }
	    Collections.sort(l);
	    long ans=1;
	    for(int i=0; i<l.size();i++) {
	    	long v=l.get(i);
	    	if(v>=N) {
	    		ans=M/v;
	    		break;
	    	}
	    }

	    System.out.print(ans);
	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}
}