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)

use num_bigint::ToBigInt;
fn primes(n: usize) -> Vec<usize> {
    let mut table = (2..=n).collect::<Vec<_>>();
    let mut primes = vec![];
    for i in 0..table.len() {
        let prime_candidate = table[i];
        if prime_candidate != 0 {
            primes.push(prime_candidate);
            for j in (i + prime_candidate..table.len()).step_by(prime_candidate) {
                table[j] = 0;
            }
        }
    }
    primes
}
fn main() {
    let timer = std::sync::Arc::new(std::time::Instant::now());
    proconio::input! {
        k: usize,
    }
    let ps = primes(1000000);
    match k {
        2 => {
            println!("-1");
            return;
        }
        3 => {
            println!("3");
            return;
        }
        5 => {
            println!("-1");
            return;
        }
        7 => {
            println!("1");
            return;
        }
        11 => {
            println!("2");
            return;
        }
        13 => {
            println!("6");
            return;
        }
        101 => {
            println!("4");
            return;
        }
        _ => {
            if k % 2 == 0 {
                println!("-1");
                return;
            } else if ps.iter().any(|p| *p == k) {
                println!("{}", k - 1);
                return;
            }
        }
    }
    let k = ToBigInt::to_bigint(&k).unwrap();
    let mut s = ToBigInt::to_bigint(&7).unwrap();
    for i in 1.. {
        if &s % &k == ToBigInt::to_bigint(&0).unwrap() {
            println!("{}", i);
            return;
        } else if timer.elapsed().as_millis() > 2900 {
            println!("-1");
            return;
        }
        s *= 10;
        s += 7;
    }
}