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 Program
{
	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]);

				// Mの約数のうちM/N以下の物を探す

				// Mの約数を探す
				int max = (int)Math.Sqrt(M);
				List<int> div = new List<int>();
				div.Add(1);
				for(int i=2; i<= max; i++)
				{
					if(M%i == 0)
					{
						div.Add(i);
						div.Add(M/i);
					}
				}

				div.Sort();
				for(int i=div.Count - 1; i>=0; i--)
				{
					if(div[i] <= M/N)
					{
						Console.WriteLine(div[i] + "");
						break;
					}
				}
    }

		class point
		{
			public int x{set; get;}
			public int y{set; get;}
			public int h{set; get;}
		}
}