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.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.Scanner;

public class Main {

    private Scanner stdin;
    private PrintWriter stdout;

    public void execute() {
        this.stdin = new Scanner(new BufferedInputStream(System.in));
        this.stdout = new PrintWriter(new BufferedOutputStream(System.out));

        while (this.stdin.hasNext()) {
            int n = stdin.nextInt();
            int m = stdin.nextInt();
            int foo = 0;
            for (int i = 1; i * i <= m; ++i) {
                if (m % i != 0) continue;
                int j = m / i;
                if (i >= n) foo = Math.max(j, foo);
                if (j >= n) foo = Math.max(i, foo);
            }
            this.stdout.printf("%d\n", foo);
        }

        this.stdin.close();
        this.stdout.close();
    }

    public static void main(String[] args) throws Exception {
        Main instance = new Main();
        instance.execute();
    }

}