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 std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        mut k: usize,
    }
    if k % 7 == 0 {
        k /= 7;
    }

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

    let mut rems = vec![0; 1000001];
    rems[1] = 1;
    for i in 2..rems.len() {
        rems[i] = rems[i-1] * 10 % k;
    }
    for i in 1..rems.len() {
        rems[i] += rems[i-1];
        rems[i] %= k;
    }

    for i in 1..rems.len() {
        if rems[i] == 0 {
            println!("{}", i);
            return;
        }
    }
    println!("-1");

}