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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.math.BigDecimal;
import java.util.Scanner;

public class Main {

    public static final int MOD = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = Long.parseLong(sc.next());
        String s = String.valueOf(n);
        char c = s.charAt(s.length() - 1);
        if (c != '1' && c != '3' && c != '7' && c != '9') {
            System.out.println(-1);
            return;
        }
//        if (!isPrime(n)) {
//            System.out.println(-1);
//            return;
//        }
//        if (n >= 1019) {
//            System.out.println(n - 1);
//            return;
//        }
        var nn = new BigDecimal(n);
        BigDecimal num = new BigDecimal(7);
        var ten = new BigDecimal(10);
        var seven = new BigDecimal(7);
        int cnt = 1;
        while(true) {
            if (num.remainder(nn).equals(BigDecimal.ZERO)) {
                System.out.println(cnt);
                return;
            }
            num = num.multiply(ten).add(seven);
            cnt++;
            if (num.toString().length() > 999983) {
                System.out.println(-1);
                return;
            }
        }
    }

    private static boolean isPrime(long n) {
        for (long i = 2; i <= n / i; i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return n != 1;
    }
}