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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        static List<ulong> Divisor(ulong input)
        {
            List<ulong> result = new List<ulong>();

            for (ulong i = 2; i * i <= input; i++)
            {
                if (0 == input % i)
                {
                    result.Add(i);
                    if (i * i != input)
                    {
                        result.Add(input / i);
                    }
                }
            }

            return result;
        }

        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int N = int.Parse(s[0]);
            int M = int.Parse(s[1]);

            List<ulong> div = Divisor((ulong)M);
            div.Sort();

            int ans = 1;
            int index = 0;
            for(index = 0; index < div.Count; index++)
            {
                if ((int)div[index] >= N)
                {
                    break;
                }
            }

            ans = M / (int)div[index];
            Console.WriteLine(ans);
        }
    }
}