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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System.Collections.Generic;
using static System.Math;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        var a = getDiv(m);
        var b = m / n;
        var ans = 0;
        foreach (var x in a)
            if (x <= b) ans = Max(ans, x);
        Console.WriteLine(ans);
    }
    public static List<int> getDiv(int n)
    {
        var ans = new List<int>();
        for (int i = 1; i <= Sqrt(n) + 1; i++)
        {
            if (n % i == 0)
            {
                ans.Add(i);
                if (n != i * i) ans.Add(n / i);
            }
        }
        return ans;
    }
}