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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
    //static List<string> str = new List<string>();
	static void Main(string[] args)
	{
		// 入力フェーズ
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        int M = int.Parse(input[1]);
        
        // N/M以下で最大の約数を返す
        int ret = func(M, M/N);

        //出力
        Console.WriteLine(ret);
    }

    static int func(int M, int g)
    {
        if(M%g == 0)
        {
            return g;
        }
        else
        {
            return func(M, g-1);
        }
    }

}