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 ConsoleApp1
{
	class Program
	{
		static void Main(string[] a_asArgs)
		{
			int[] l_aiInput = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
			int l_iN = l_aiInput[0];
			int l_iM = l_aiInput[1];

			if (l_iN == 1)
			{
				Console.WriteLine(l_iM);
				return;
			}

			for (int l_iD = l_iM / l_iN; l_iD > 1; l_iD--)
			{
				if (l_iM % l_iD == 0)
				{
					Console.WriteLine(l_iD);
					break;
				}
			}
		}
	}
}