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.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class ABC
	{
		static readonly int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			//int n = int.Parse(Console.ReadLine());
			//string s = Console.ReadLine();
			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
			int n = vs[0];
			int m = vs[1];
			int ans = 0;
			for (int i = (int)Math.Sqrt(m); i > 0; i--) {
				if (m % i == 0) {
					if (m / i >= n) {
						ans = i;
						break;
					}
				}
			}
			Console.WriteLine(ans);


			Console.Out.Flush();
		}
	}
}