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: Accepted)

#include <math.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define PI acos(-1)
typedef long long int ll;
typedef long double ld;

int main(void) {
  int   scan;

  ll    answer;
  ll    k; 
  answer = 1;
  scan = scanf("%lld", &k);

  ll    mod;
  mod = k % 10;
  if (mod == 0 || mod == 2 || mod == 4 || mod == 5 || mod == 6 || mod == 8) {
    printf("-1");
    return (0);
  }

  if (k % 7 == 0) {
    k = k / 7;
  } 
  
  ll  p;
  ll  l;
  l = 9 * k;
  p = 1;
  while (1) {
    p = 10 * p % l;
    if (p == 1) {
      break ;
    } else {
      answer++;
    }
  }

  printf("%lld", answer);

  return (0);
}