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) {
		Main m = new Main();
		m.run();
	}

	Scanner sc = new Scanner(System.in);

	void run() {

		int k = sc.nextInt();
		
		int min = 45;
		for(int i = 1 ; i < k ; i++){
			long v = (long)k*i;
			int val = calc(v , min);
			min = Math.min(min, val);
		}
		System.out.println(min);
		
	}
	
	int calc(long v, int min){
		int d = 0;
		while(v > 0 && min > d){
			d += v%10;
			v = v/10;
		}
		return d;		
	}
	
}