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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        long N = scan.nextLong();
        long M = scan.nextLong();
        if (N == 1) {
            System.out.println(M);
            return;
        }
        List<Long> divisors = this.divisor(M);
        long answer = 1;
        for (long i : divisors) {
            if (M < i * N) {
                continue;
            }
            long x = M - i * (N - 1);
            if (x % i == 0 && x > 0) {
                answer = Math.max(answer, i);
            }
        }
        System.out.println(answer);
    }
    private List<Long> divisor(long M) {
        List<Long> list = new ArrayList<>();
        for (long i = 2; i * i <= M; i++) {
            if (M % i != 0) {
                continue;
            }
            list.add(i);
            long j = M / i;
            if (i != j) {
                list.add(j);
            }
        }
        return list;
    }
}