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: Wrong Answer)

#![allow(non_snake_case)]
#![allow(unused_imports)]
#![allow(dead_code)]

use proconio::{input, fastout};
use proconio::marker::*;
use whiteread::parse_line;
use std::collections::*;
use num::*;
use num_traits::*;
use superslice::*;
use std::ops::*;

use itertools::Itertools;
use itertools_num::ItertoolsNum;

pub fn prime_factorize<T: PrimInt + NumAssign>(mut n: T) -> Vec<(T, T)> {
    let mut res: Vec<(T, T)> = Vec::new();
    let mut i: T = one::<T>().signed_shl(1);
    while i * i <= n {
        if n % i == zero() {
            let mut ex = zero::<T>();
            while n % i == zero() {
                ex += one();
                n = n / i;
            }
            res.push((i, ex));
        }
        i += one();
    }
    if n != one() {
        res.push((n, one()))
    }
    res
}


#[fastout]
fn solve() {
    const MOD: usize = 1_000_000_007;
    const INF: usize = std::usize::MAX;
    
    input!{
        k: usize,
    }

    let mut x = 7 % k;
    let mut set: HashSet<usize> = HashSet::new();
    
    let mut ans = 1;

    for _ in 0..k {
        set.insert(x);
        x = (10 * x + 7) % k;
        // dbg!(&x);
        ans += 1;
        
        if x == 0 {
            set.insert(x);
            break;
        }
    }

    if set.contains(&0) {
        println!("{}", ans)
    } else {
        println!("{}", -1)
    }
}

fn main() {
    solve()
}

#[cfg(test)]
mod test {
    use super::solve;
}