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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
            var input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            int n = (int)input[0];
            long m = input[1];

            var prev = m;
            for (int i = 1; i <= 100000; i++)
            {
                if (m % i != 0) continue;
                if(m / i < n)
                {
                    Console.WriteLine(prev);
                    return;
                }
                prev = i;
            }


            for (long i = n; i <= m; i++)
            {
                if (m % i != 0) continue;

                var result = m / i;
                Console.WriteLine(result);
                return;
            }
    }
}