Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;

    const int N = 100000;
    void solve()
    {
        int K = cin.nextint;
        if (K % 9 == 0)
        {
            long d = 0;
            while (K > 0)
            {
                d += K % 10;
                K /= 10;
            }
            WriteLine(d);
            return;
        }


        eratos(K);

        var L = new List<long>();
        for (int i = 1; i < prime.Count; i++)
        {
            if (K % prime[i] == 0)
            {
                L.Add(prime[i]);
            }
        }
        if (L.Count == 0)
        {
            WriteLine(1);
            return;
        }
        long ans = long.MaxValue;
        for (int i = 0; i < L.Count; i++)
        {
            while (true)
            {
                long sum = 0;
                while (L[i] > 0)
                {
                    sum += L[i] % 10;
                    L[i] /= 10;
                }
                if (sum <= 10)
                {
                    ans = Math.Min(ans, sum);
                    break;
                }
                L[i] = sum;
            }
        }
        WriteLine(ans);


    }

    List<int> prime;
    bool[] is_prime;
    void eratos(int n)
    {
        prime = new List<int>();
        is_prime = new bool[n + 1];
        for (int i = 0; i <= n; i++) is_prime[i] = true;
        is_prime[0] = is_prime[1] = false;
        for (int i = 0; i <= n; i++)
        {
            if (is_prime[i])
            {
                prime.Add(i);
                for (int j = 2 * i; j <= n; j += i) is_prime[j] = false;
            }
        }
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}