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(unused_imports)]
#![allow(unused_macros)]
// use proconio::input;
use std::cmp::{Ordering::*, Reverse};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, VecDeque};
use std::io::{self, BufWriter, Write};
use std::str::{self, SplitAsciiWhitespace};

// I have no idea what I'm doing

macro_rules! answer {
    ($out:ident, $ans:expr) => {
        writeln!($out, "{}", $ans)
    };
}

fn main() -> Result<(), io::Error> {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut scan = UnsafeScanner::new(stdin.lock());
    let mut out = BufWriter::new(stdout.lock());

    let k: i32 = scan.token();
    let mut m = 0;
    let mut ans = None;
    for i in 1..=k {
        m *= 10;
        m += 7;
        m %= k;

        if m == 0 {
            ans = Some(i);
            break;
        }
    }

    answer!(out, ans.unwrap_or(-1))
}

///////////////////////////////////////////////////////////////////////////////////////////////////

/// Mostly copied from https://github.com/EbTech/rust-algorithms/blob/master/src/scanner.rs
/// Same API as Scanner but nearly twice as fast, using horribly unsafe dark arts
/// **REQUIRES** Rust 1.34 or higher
pub struct UnsafeScanner<R> {
    reader: R,
    buf_str: Vec<u8>,
    buf_iter: SplitAsciiWhitespace<'static>,
}

impl<R: io::BufRead> UnsafeScanner<R> {
    pub fn new(reader: R) -> Self {
        Self {
            reader,
            buf_str: vec![],
            buf_iter: "".split_ascii_whitespace(),
        }
    }

    /// This function should be marked unsafe, but noone has time for that in a
    /// programming contest. Use at your own risk!
    pub fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buf_iter.next() {
                return token.parse().ok().expect("Failed parse [Scanner]");
            }
            self.buf_str.clear();
            self.reader
                .read_until(b'\n', &mut self.buf_str)
                .expect("Failed read");
            self.buf_iter = unsafe {
                let slice = str::from_utf8_unchecked(&self.buf_str);
                std::mem::transmute(slice.split_ascii_whitespace())
            }
        }
    }

    pub fn pair<T: str::FromStr>(&mut self) -> (T, T) {
        (self.token(), self.token())
    }
}

// aka #![feature(bool_to_option)]
trait BoolThen {
    fn then_<T>(self, f: impl FnOnce() -> T) -> Option<T>;
}

impl BoolThen for bool {
    fn then_<T>(self, f: impl FnOnce() -> T) -> Option<T> {
        if self {
            Some(f())
        } else {
            None
        }
    }
}

trait BoolToYes {
    fn yes(self) -> &'static str;
}

impl BoolToYes for bool {
    fn yes(self) -> &'static str {
        match self {
            true => "Yes",
            false => "No",
        }
    }
}