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 C# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
public class Hello{
    public static void Main()
    {
        ulong K = ulong.Parse(System.Console.ReadLine());
        if (K % 2 == 0)
        {
            Console.WriteLine(-1);
            return;
        }
        long count = (long)Math.Log10(K) + 1;
        ulong v = 7; 
        for (int i = 1; i < count; i++)
        {
            v = v * 10 + 7;
        }
        while (true)
        {
            if (v % K == 0)
            {
                Console.WriteLine(count);
                return;
            }
            v = v * 10 + 7;
            count++;
        }
    }
}