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)]
use proconio::{input, fastout};
use proconio::marker::*;

#[fastout]
fn main() {
    input! {
    k: usize
    }
    let dk = if k % 7 == 0 {
        k / 7
    } else {
        k
    };
    if gcd(&dk, &10) != 1 {
        println!("-1");
        return
    }
    let mut s = 1 % dk;
    for i in 1.. {
        if s == 0 {
            println!("{}", i);
            return
        }
        s = (10 % dk * s + 1 % dk) % dk;
    }
}

// O(log(N))
fn gcd(a: &usize, b: &usize) -> usize {
    let (mut x, mut y) = if a < b { (*b, *a) } else { (*a, *b) };
    let mut r = x % y;
    while r != 0 {
        x = y;
        y = r;
        r = x % y;
    }
    y
}