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 <bits/stdc++.h>
using namespace std;
using namespace std::chrono;

int main() {
  int K;
  cin >> K;
  int cnt = 0, now = 0;
  auto start = system_clock::now();
  while (++cnt) {
    now = (now * 10 + 7) % K;
    if (now == 0) return cout << cnt << "\n", 0;
    if (static_cast<double>(duration_cast<milliseconds>(system_clock::now() - start).count() / 1000.0) > 1.99) {
      return cout << -1 << "\n", 0;
    }
  }
}