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)

use proconio::input;
//use proconio::marker::{Bytes, Chars};

// x ** n % mods を求める
pub fn mod_pow(x: i64, n: i64, mods: i64) -> i64 {
    if n == 0 {
        return 1;
    }
    let mut res = mod_pow(x * x % mods, n / 2, mods);
    if n % 2 == 1 {
        res = res * x % mods;
    }
    return res;
}

// (1/n) % mods を求める
pub fn mod_inv(n: i64, mods: i64) -> i64 {
    return mod_pow(n, mods-2, mods);
}

// nCk % mods を求める
pub fn mod_comb(n: i64, k: i64, mods: i64) -> i64 {
    let sum1 = (n-k+1..n+1).fold(1, |ac, x| ac * x % mods);
    let sum2 = (1..k+1).fold(1, |ac, x| ac * x % mods);
    return sum1 * mod_inv(sum2, mods) % mods;
}

// nCk の組み合わせを列挙する
pub fn combination(n: usize, k: usize) -> Vec<Vec<usize>> {
    let mut ans = Vec::new();
    if k == 1 {
        for i in 1..n+1 {
            let mut tmp = Vec::new();
            tmp.push(i);
            ans.push(tmp);
        }
    }
    else {
        for iter in combination(n-1, k-1) {
            let max = iter.iter().max().unwrap();
            for j in *max+1..n+1 {
                let mut tmp = iter.clone();
                tmp.push(j);
                ans.push(tmp);
            }
        }
    }
    ans
}


fn main() {
    input!{
        k: usize,
    }
    let mut div = 7 % k;
    for i in 1..1000000 {
        if div == 0 {
            println!("{}", i);
            return;
        }
        div = (div * 10 + 7) % k;
    }
    println!("-1");
}