Problem:
Score : 300 points

Problem Statement

Takahashi loves the number 7 and multiples of K.

Where is the first occurrence of a multiple of K in the sequence 7,77,777,\ldots? (Also see Output and Sample Input/Output below.)

If the sequence contains no multiples of K, print -1 instead.

Constraints

1 \leq K \leq 10^6

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4.)

Sample Input 1

101

Sample Output 1

4

None of 7, 77, and 777 is a multiple of 101, but 7777 is.

Sample Input 2

2

Sample Output 2

-1

All elements in the sequence are odd numbers; there are no multiples of 2.

Sample Input 3

999983

Sample Output 3

999982

Solution in C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int main(void){
    unsigned int m;
    scanf("%d", &m);
    
    if(m%2==0||m%5==0){
        printf("-1");
        return 0;
    }
    
    unsigned int n,i,k,s;
    
    for(n=0;;n++){
    
    for(i=0;i<=n;i++){
        if(i==0){
        s=7%m;
        k=7;
        }else{
        k*=10;
        k%=m;
        s+=k;
        s%=m;
        }   
    }
    
    if(s==0){
      printf("%d",n+1);
      break;
    }
  }
  return 0;
}