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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

long long int hen(long long int a) {
	if (a == 0) {
		return 0;
	}
	else {
		return (a % 10) + hen(a / 10);
	}
}


int main() {

	long long int k;

	cin >> k;

	long long int MIN = hen(k);

	for (long long int i = 1; i < 1000000; i++) {
		MIN = min(MIN, hen(k*i));
	}

	cout << MIN << endl;

	return 0;
}