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: Runtime Error)

#include <stdio.h>

int digitSum(int n){
	int sum = 0;
	while (n >= 1){
		sum += (n % 10);
		n/=10;
	}
	return sum;
}

void main(){
	int K,k, i = 1;
	int cnt = 1;
	do{
		printf("K>>"); scanf("%d", &k);
	} while (k < 2 || k>100000);
	K = k;
	int min = digitSum(K);
	while (i < 100000){
		K = K*i;
		if (digitSum(K) < min) {
			min = digitSum(K); cnt=i;
		}
		if (min <= k) break;
		i++;
	}
	printf("Output:%d when %d * %d = %d\n", min,k,cnt,k*cnt);
}