Question

The problem is as follows:

There is one friendly number and N unfriendly numbers. We want to find how many numbers are there which exactly divide the friendly number, but does not divide any of the unfriendly numbers.

Input Format:
The first line of input contains two numbers N and K seperated by spaces. N is the number of unfriendly numbers, K is the friendly number.
The second line of input contains N space separated unfriendly numbers.

Output Format:
Output the answer in a single line.

Constraints:
1 <= N <= 10^6
1 <= K <= 10^13
1 <= unfriendly numbers <= 10^18

Sample Input:
8 16
2 5 7 4 3 8 3 18

Sample Output:
1

Explanation :
Divisors of the given friendly number 16, are { 1, 2, 4, 8, 16 } and the unfriendly numbers are {2, 5, 7, 4, 3, 8, 3, 18}. Now 1 divides all unfriendly numbers, 2 divide 2, 4 divide 4, 8 divide 8 but 16 divides none of them. So only one number exists which divide the friendly number but does not divide any of the unfriendly numbers. So the answer is 1.   

Following is my C# solution:

class Solution
{
    static void Main(string[] args)
    {
        string firstLine = Console.ReadLine();
        string[] firstLineItems = firstLine.Split(' ');

        ulong friendlyNum = Convert.ToUInt64(firstLineItems[1]);
        int noOfunf = Convert.ToInt32(firstLineItems[0]);

        string secondLine = Console.ReadLine();
        string[] secondLineItems = secondLine.Split(' ');

        List<ulong> unfriendlyNumbersArray = new List<ulong>(noOfunf);

        foreach (string str in secondLineItems)
        {
            unfriendlyNumbersArray.Add(Convert.ToUInt64(str));
        }

        List<ulong> divisors = CalculateDivisors(friendlyNum);

        Console.WriteLine(finalCall(divisors, unfriendlyNumbersArray));
    }

    private static List<ulong> CalculateDivisors(ulong number)
    {
        List<ulong> factors = new List<ulong>();

        for (ulong factor = 1; factor * factor <= number; ++factor)
        {
            if (number % factor == 0)
            {
                factors.Add(factor);
                if (factor * factor != number)
                {
                    factors.Add(number / factor);
                }
            }
        }
        return factors;
    }

    private static long finalCall(List<ulong> divisors, List<ulong> unfriendlyNumbersArray)
    {
        long output = 0;
        var unfriendlyNumbers = (from i in unfriendlyNumbersArray select i).Distinct();

        foreach (ulong divisor in divisors)
        {
            var test = unfriendlyNumbers.Where(number => number % divisor == 0).ToList();
            output += (test.Count == 0) ? 1 : 0;
        }
        return output;
    }
}

Only first 3 test cases pass. 4th one is killed, 5th and 6th one gives me parsing exception for string.

Exception for 5th and 6th ones:

Unhandled Exception: System.FormatException: Input string was not in the correct format
    at System.UInt64.Parse (System.String s) [0x00000] in :0 
    at System.Convert.ToUInt64 (System.String value) [0x00000] in :0 
    at Solution.Main (System.String[] args) [0x00000] in :0 
    [ERROR] FATAL UNHANDLED EXCEPTION: System.FormatException: Input string was not in the     correct format
    at System.UInt64.Parse (System.String s) [0x00000] in :0 
    at System.Convert.ToUInt64 (System.String value) [0x00000] in :0 
    at Solution.Main (System.String[] args) [0x00000] in :0

Answer 1

I was able to solve this problem based on the following link.
I was really amazed by the in-depth understanding of number theory of the author of the above link.
There is nothing wrong in the above algorithm. just that it will not solve the problem within 5 seconds, the constraint which we we have abide by.