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)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        k: usize,
    }
    if gcd(k, 2) != 1 || gcd(k, 5) != 1 {
        println!("-1");
        return;
    }
    let mut sevens = 7 % k;
    let mut count = 1;
    while sevens != 0 {
        sevens *= 10;
        sevens += 7;
        sevens %= k;
        count += 1;
    }
    println!("{}", count);
}

fn gcd(x: usize, y: usize) -> usize {
    if x < y {
        return gcd(y, x);
    } else if y == 0 {
        return x;
    } else {
        return gcd(y, x - (x / y) * y);
    }
}