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 <iostream>
#include <algorithm>
#include <sstream>
#include <stdio.h>
#include <string>
#include <vector>
#include <math.h>
using namespace std;

int main()
{
  int k;
  cin >> k;

  if (k % 2 == 0)
  {
    cout << -1 << "\n";
  }
  else
  {
    int count = 1;
    long long num = 7;
    while (true)
    {
      if (num % k == 0)
      {
        cout << count << "\n";
        break;
      }
      count++;
      num = (num * 10 + 7) % k;
    }
  }

  return 0;
}