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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int num = s.nextInt();
		int valLen = String.valueOf( num ).length(); 
		System.out.print(findMin(num, (long) Math.pow(10,valLen)));
//		int returnNum = 0;
//		System.out.println(digitSum(num));
//		if(num %9 ==0){
//			returnNum = digitSum(num);
//		}else if(num %3==0){
//			returnNum = findMin(num, 3);
//		}else{
//			returnNum = findMin(num, 9);
//		}
//		System.out.print(returnNum);
	}
	
	public static int findMin(int num, long times){
		int min = Integer.MAX_VALUE;
		for (long i = 1; i <= times; i++) {
			int digitSum= digitSum(num*i);
			if(min > digitSum){
				min = digitSum;
			}
		}
		return min;
	}
	
	public static int digitSum(long num){
		int sum=0;
		String str =  String.valueOf(num);
		for(int i=0; i< str.length(); i++){
			sum += str.charAt(i)-'0';
			}
		return sum;
	}

}