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;

namespace CSharpSample01
{
    
    class Program
    {
        
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            long N = long.Parse(input[0]);
            long M = long.Parse(input[1]);

            long max_D = M / N;

            long ans = 1;
            
            for(long i = 1; i <= Math.Sqrt(M); i++)
            {
                if(i > max_D)
                {
                    break;
                }
                else
                {
                    if(M % i == 0)
                    {
                        ans = i;
                    }
                }
            }


            Console.WriteLine(ans);

        }
    }
}