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.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        long k = sc.nextInt();

        if(k % 2 == 0){
            System.out.println(-1);
            return;
        }

        StringBuilder seven = new StringBuilder("7");
        BigDecimal bd = new BigDecimal(seven.toString());
        BigDecimal zero = new BigDecimal(0);
        BigDecimal kbd = new BigDecimal(k);
        long ans = 1;
        while(!bd.remainder(kbd).equals(zero)){
            seven.append('7');
            bd = new BigDecimal(seven.toString());
            ans++;
        }

        System.out.println(ans);

    }
}