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 1.8.0) (judge verdict: Accepted)

import java.util.HashSet;
import java.util.Scanner;

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

            HashSet<Long> used = new HashSet<Long>();
            long l7 = 7;
            for (int i = 1;;) {
                if (l7 % K == 0) {
                    System.out.println(i);
                    return;
                }
                if (l7 < K) {
                    l7 = l7 * 10 + 7;
                    i++;
                    if (!used.add(l7)) {
                        System.out.println(-1);
                        return;
                    }
                } else {
                    l7 %= K;
                }
            }
        }
    }
}