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::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("faild to read char") as char)
        .take_while(|c| !c.is_whitespace())
        .collect();
    token
        .parse()
        .ok()
        .expect("faild to parse token")
}

fn main(){
    let n: u64 = read();
    let mut ret = 1;
    let mut base = 7;

    if n % 2 == 0 || n% 5 == 0 {
        println!("-1");
        return;
    }

    loop {
        if base % n == 0 {
            break;
        }
        ret += 1;
        base = (base * 10) % n;
        base = (base + 7) % n;
    }
    println!("{}", ret);
}

fn inverse(n1: u64) -> u64 {
    let mut n = n1;
    let mut ret = 1;

    for i in 2..n1 {
        if n < i * i {
            break;
        }

        let mut pow = 0;
        while n % i == 0 {
            n /= i;
            pow += 1;
            ret *= i;
        }

        if pow > 0 {
            ret /= i;
            ret *= i - 1;
        }
    }

    if n > 1 {
        ret *= n - 1;
    }
    ret
}