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: Time Limit Exceeded)

import java.util.Scanner;
import java.math.BigInteger;

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

    //input
    String newString = sc.next();
    BigInteger k = new BigInteger(newString);

    //output
    BigInteger num = new BigInteger("7");
    for(int i = 1; i < 1000000; i++){
      if( num.remainder(k).equals(new BigInteger("0")) ){ //if divisible
        System.out.println(i);
        //System.out.println(num);
        System.exit(0);
      }

      //add 7 to end
      num = num.multiply(new BigInteger("10"));
      num = num.add(new BigInteger("7"));
      //System.out.println(num);
    }

    System.out.println("-1");

  }
}