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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace atcoder174
{
    class Program
    {
        static void Main(string[] args)
        {
            var k = int.Parse(Console.ReadLine()); // kの倍数が登場するのは何項目か

            var remainder = 7 % k;

            // k以上辿っていたらループしているため処理を終了する
            for (var i =1; i<k+1 ;i++ )
            {
                if (remainder == 0)
                {
                    Console.WriteLine(i);
                    return;
                }

                // 項数が増えるたびに数はn * 10 + 7増えるため
                // 余りも同じだけ増える。それをkで割った余りを再び計算する 
                remainder = (remainder * 10 + 7) % k;

            }

            // 割り切れなかった場合は、-1を出力する
            Console.WriteLine(-1);
        }
    }
}