Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::iter;
#[allow(unused_imports)]
use std::mem::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::usize;

#[allow(unused_macros)]
macro_rules! read_cols {
    ($($t:ty),+) => {{
        let mut line = String::new();
        stdin().read_line(&mut line).unwrap();

        let mut it = line.trim()
            .split_whitespace();

        ($(
            it.next().unwrap().parse::<$t>().ok().unwrap()
        ),+)
    }}
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();
    line.trim().to_string().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();

    line.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn digit_sum(mut n: i64) -> i64 {
    let mut s: i64 = 0;

    while n > 0 {
        s += n % 10;
        n /= 10;
    }

    s
}

fn main() {
    let k = read::<i64>();

    if k == 100000 {
        println!("1");
        return;
    }

    let mut visited = vec![false; 100000];
    let mut m = k;
    let mut ans = 100;
    while !visited[(m % 100000) as usize] {
        visited[(m % 100000) as usize] = true;

        let s = digit_sum(m);

        // println!("{} {}", m, s);

        if s < ans {
            ans = s;
        }

        m = (m + k);
    }

    println!("{}", ans);
}