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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#define int long long

int digit_sum(int K){
	int ans;
	for(ans = 0; K > 0; K /= 10){
		ans += K % 10;
	}
	return ans;
}

int min(int a, int b){
	return a <= b ? a : b;
}

signed main(){
	int K, i, ans = digit_sum(K);
	scanf("%lld", &K);
	for(i = 1; i <= 1000000; i++){
//		printf("digit_sum(K * %lld) = %lld\n", i, digit_sum(K * i));
		ans = min(ans, digit_sum(K * i));
//		printf("ans = %lld\n", ans);
	}
	printf("%lld\n", ans);
	return 0;
}