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;
class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		long A = long.Parse(str[0]);
		long B = long.Parse(str[1]);
		var list = enum_div(B);
		list.Sort();
		long ans = 1;
		for(var i=0;i<list.Count;i++){
			if(list[list.Count-1-i] <= B / A){
				ans = list[list.Count-1-i];
				break;
			}
		}
		Console.WriteLine(ans);
	}
	
	public static List<long> enum_div(long n){
		var list = new List<long>();
		for(var i=1;i*i<=n;i++){
			if(n%i==0){
				list.Add(i);
				if(i*i!=n){
					list.Add(n-i);
				}
			}
		}
		return list;
	}
}