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<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<queue>
using namespace std;

typedef long long ll;
typedef pair<int,int> P;

#define pb push_back
#define fr first
#define sc second

ll f(ll x){
	if(x < 10)return x;
	return x%10+f(x/10);
}

int main(){
	ll K;
	cin >> K;
	
	while(K%2 == 0)K /= 2;
	while(K%5 == 0)K /= 5;
	
	ll ret = 10000000000;
	for(int i = 1 ; i <= K ; i ++){
		ret = min( ret , f(K*i) );
	}
	cout << ret << endl;
}