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 Rust (1.42.0) (judge verdict: Accepted)

use std::collections::HashSet;

fn input_line() -> Vec<String> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).unwrap();
  return buf
    .split_whitespace()
    .map(|word| String::from(word))
    .collect();
}

fn main() {
  let inputs = input_line();
  let k: i64 = inputs[0].parse().unwrap();
  let mut value: i64 = 7;
  let mut i: i64 = 1;
  let mut set: HashSet<i64> = HashSet::new();
  let mut ans = -1;
  loop {
    let m = value % k;
    if m == 0 {
      ans = i;
      break;
    }
    if set.contains(&m) {
      break;
    }
    set.insert(m);
    value = (value * 10 + 7) % k;
    i += 1;
  }

  println!("{}", ans);
}