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>

#define rep(i, ss, ee) for (int i = ss; i < ee; ++i)
using namespace std;

int k;
void input() { cin >> k; }

void exit_end(int ans) {
  cout << ans << endl;
  exit(0);
}

void solve() {
  vector<int> v(k + 1, -1);
  if (k % 2 == 0) exit_end(-1);
  v[1] = 7 % k;
  rep(i, 2, k + 1) v[i] = (v[i - 1] * 10 + 7) % k;
  rep(i, 1, k + 1) {
    if (v[i] == 0) { exit_end(i); }
  }
  exit_end(-1);
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  input();
  solve();
}