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) {
    Scanner sc = new Scanner(System.in);
    long k = sc.nextLong();
    int ans = Integer.MAX_VALUE;
    for(int i = 1; i <= 100000; i++) {
      long t = k * (long)i;
      int temp = 0;
      for(int j = 0; j < 20; j++) {
        if(t > 0) {
          temp += (int)(t % 10);
          t /= 10;
        } else {
          break;
        }
      }
      ans = Math.min(ans, temp);
    }
    System.out.println(ans);
  }
}