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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        
        Set<Long> digitS = new HashSet<>();
        int i = 1;
        while(true) {
           long ds = digitSum(k * i);
           if(ds == k) break;
           digitS.add(ds);
           i++;
        }
        long min = Long.MAX_VALUE;
        for(long d : digitS)
          min = Math.min(min, d);

        System.out.println(min);
    }

    private static long digitSum(long num) {
      long sum = 0;
      while(num > 0) {
        sum += (num % 10);
        num /= 10;
      }
      return sum;
    }
}