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;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
		long n = long.Parse(input[0]);
		long m = long.Parse(input[1]);
    List<long> divisorList = new List<long>();

    for(long answer = (long)Math.Sqrt(m)+1; answer > 0; answer--)
    {
      if(m % answer == 0)
      {
        divisorList.Add(answer);
        divisorList.Add(m/answer);
      }
    }
    divisorList.Sort((a, b) => a.CompareTo(b));

    for(int i = divisorList.Count()-1; i >= 0; i--)
    {
      if(divisorList[i] * n <= m)
      {
        Console.WriteLine(divisorList[i]);
        break;
      }
    }
    
	}
}