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.BigInteger;
import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int k = sc.nextInt();
        long ans = -1l;
        if(k % 2 == 0) {
            System.out.println(-1);
            return;
        }
        if(k == 7 || k == 1) {
            System.out.println(1);
            return;
        }
        BigInteger tmp2 = new BigInteger("7");
        BigInteger kk = new BigInteger(Integer.toString(k));
        BigInteger k10 = new BigInteger("10");
        BigInteger k7 = new BigInteger("7");
        long count = 0l;
        while(count < k + 2) {
            if(tmp2.remainder(kk).equals(BigInteger.ZERO)) {
                String s = tmp2.toString();
                ans = s.length();
                break;
            }
            tmp2 = tmp2.multiply(k10);
            tmp2 = tmp2.add(k7);
        }
        System.out.println(ans);
    }
}