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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class Procon
{
    public Procon() { }
    static void Main(string[] agrs)
    {
        new Procon().Do();
    }

    Scanner cin;

    public void Do()
    {
        cin = new Scanner();
        long N = cin.nextLong();
        long M = cin.nextLong();

        double X = Math.Sqrt(M);
        long ans = 0;

        for (int i = 1; i < X; i++)
        {
            if (M % i == 0)
            {
                if (i >= N)
                {
                    ans = Math.Max(M / i, ans);
                }
                else if (M / i >= N)
                {
                    ans = Math.Max(i, ans);
                }
            }
        }

        Console.WriteLine(ans);
    }
}

class Scanner
{
    string[] s;
    int i;
    int max_i;

    public Scanner()
    {
        s = new string[0];
        max_i = 0;
        i = 0;
    }

    public string nextString()
    {
        if (i >= s.Length)
        {
            s = Console.ReadLine().Split(' ');
            max_i = s.Length;
            i = 0;
            if (max_i == 0)
            {
                return "";
            }
            return s[i++];
        }
        else
        {
            return s[i++];
        }
    }

    public int nextInt()
    {
        return int.Parse(nextString());
    }


    public long nextLong()
    {
        return long.Parse(nextString());
    }

    public double nextDouble()
    {
        return double.Parse(nextString());
    }

    public string[] arrayString()
    {
        return Console.ReadLine().Split(' ');
    }

    public int[] arrayInt()
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] array = new int[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = int.Parse(str[i]);
        }
        return array;
    }

    public long[] arrayLong()
    {
        string[] str = Console.ReadLine().Split(' ');
        long[] array = new long[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = long.Parse(str[i]);
        }
        return array;
    }

    public double[] arrayDouble()
    {
        string[] str = Console.ReadLine().Split(' ');
        double[] array = new double[str.Length];
        for (int i = 0; i < str.Length; i++)
        {
            array[i] = double.Parse(str[i]);
        }
        return array;
    }
}