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)

#![allow(dead_code, unused_imports, deprecated)]
use std::cmp::{max, min, Reverse};
use std::collections::*;
use maplit::*;
use num::Integer;
use proconio::input;
use proconio::marker::*;
use proconio::fastout;

const INF : usize = 1000000007;

fn main() {
  input! {
    k : usize,
  };

  let mut d = 7;
  let mut cur = d % k;
  let mut res = 1;
  loop {
    if cur == 0 || (k % 2 == 0 || k % 5 == 0) {
      break;
    }
    
    d = (d * 10) % k;
    cur = (cur + d) % k;
    res += 1;
  }

  if k % 2 == 0 || k % 5 == 0 {
    println!("-1");
  } else {
    println!("{}", res);
  }
}