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;

namespace AtCoder.ABC._112
{
    class d
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Trim();
            var spl = line.Split(' ');
            var N = int.Parse(spl[0]);
            var M = int.Parse(spl[1]);
            var O = (double)M / N;
            var max = 1;
            for(var i = 2; i <= O; ++i)
            {
                if (M % i == 0) max = i;
            }
            Console.WriteLine(max);
        }
    }
}