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: Time Limit Exceeded)

#[allow(unused)]
use {
    std::error::Error,
    std::fmt::Debug,
    std::str::FromStr,
    std::io::prelude::*,
    std::io::{stdin, stdout, BufReader, BufWriter},
    std::collections::HashSet,
    std::cmp::min,
};

type BoxResult<T> = Result<T, Box<dyn std::error::Error>>;


fn main() -> BoxResult<()> {
    let mut scanner = Scanner::new(stdin());
    
    let k = scanner.read::<usize>()?;

    if k % 2 == 0 {
        println!("-1");
        return Ok(());
    }

    let mut r = 7 % k;
    let mut index = 1;
    while r != 0 {
        r = (r * 10 + 7) % k;
        index += 1;
    }

    println!("{}", index);
    
    Ok(())
}

pub struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    pub fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    pub fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    pub fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    pub fn read_two<T, U>(&mut self) -> BoxResult<(T, U)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            (a, b)
        };
        self.buffer.clear();
        Ok((a, b))
    }
    pub fn read_three<T, U, V>(&mut self) -> BoxResult<(T, U, V)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            (a, b, c)
        };
        self.buffer.clear();
        Ok((a, b, c))
    }
    pub fn read_four<T, U, V, W>(&mut self) -> BoxResult<(T, U, V, W)>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
        U: FromStr + Copy,
        U::Err: Debug + Error + 'static,
        V: FromStr + Copy,
        V::Err: Debug + Error + 'static,
        W: FromStr + Copy,
        W::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let (a, b, c, d) = {
            let params = self.buffer.trim().split_whitespace().collect::<Vec<_>>();
            let a = params[0].parse()?;
            let b = params[1].parse()?;
            let c = params[2].parse()?;
            let d = params[3].parse()?;
            (a, b, c, d)
        };
        self.buffer.clear();
        Ok((a, b, c, d))
    }
    pub fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    pub fn read_matrix<T>(&mut self, lines: u64) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr + Copy,
        T::Err: Debug + Error + 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    pub fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}