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(dead_code)]

use proconio::input;
use proconio::marker::{Bytes, Chars};
use std::collections::*;

fn main() {
    input! {
        k:i64,
    }
    let ans = (0..k)
        .scan(0, |acc, x| {
            *acc = (*acc + 7 * modpow(10, x, k) % k) % k;
            Some(*acc)
        })
        .enumerate()
        .find(|(_, x)| x % k == 0);
    if let Some((n, _)) = ans {
        println!("{}", n + 1);
    } else {
        println!("{}", -1);
    }
}

fn modpow(a: i64, x: i64, m: i64) -> i64 {
    if x == 0 {
        1
    } else if x % 2 != 0 {
        a * modpow(a, x - 1, m) % m
    } else {
        let half = modpow(a, x / 2, m);
        half * half % m
    }
}