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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var array = Console.ReadLine().Split();
            int n = int.Parse(array[0]);
            long m = long.Parse(array[1]);

            List<long> divisors = new List<long>();
            for (long i = 1; i * i <= m; i++)
            {
                if (m % i == 0)
                {
                    divisors.Add(i);
                    divisors.Add(m / i);
                }
            }

            long ans = divisors.Where(d => d * n <= m).Max();
            Console.WriteLine(ans);
        }
    }
}