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<time.h>

int main(){
  static long long n,m,tmp,i=1,ii,k,res=999999999,t;
  clock_t t0,t1;
  t0=clock();
  scanf("%lld",&n);
  for(t=1;t;t+=100){
    ii=i+t;
    for(i;i<ii;++i){
      if(i%10==0)continue;
      m+=n;
      tmp=0;
      do {
	tmp+=m%10;
      } while(m/=10);
      if(res>tmp)res=tmp;
      
      t1=clock();
      
      if(clock()-t0 >1990000){
	printf("%lld\n",res);

	exit(0);
      }
    }
  }
}