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.Scanner;

class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long N = scanner.nextInt(),ans=0,i;
        //N*X -> 7*10^3+7*10^2+7*10^1+7 => 7(10^3+10^2+10^1+1) => 7(1 + 10*(10^2+10+1)) => 7(1+10+ 100*(10^2+10+1))
                                                                //7(1+10(1+10*(1+10*(1+10*())))

        if (N%7==0)
            N/=7;
        if (N%2==0) {
            System.out.println("-1");
            return;
        }

        //factor of 7?
        long cum = 0;
        for (int j = 1; j < N+10; j++) {
            cum = cum*10L+1;
            if (cum>N)
                cum=cum%N;
            if (cum==N || cum==0) {
                System.out.println(j);
                return;
            }
        }
        System.out.println("-1");
        /*
        7(1)
         7 + 10 * 7
            7 + 10 * 7 + 700
                1 + 10 + 100
         **/
        //10^x-1/9 = N*X/7, 10^x = N*X*9/7+1  =>
        //N*X => 0, 7, 7*11 , 7 * 111
        //BigInteger num = new BigInteger("7"), N1 = new BigInteger(N+""), N2 = BigInteger.ONE;
        /*for (i = 1; i <= N&&N%2==1; i++) {
            if (num.mod(N1).equals(BigInteger.ZERO))
                break;
            N2=N2.multiply(BigInteger.TEN).add(BigInteger.ONE);
            num=num.multiply(N2);
        }
        System.out.println((i==N+1||N%2==0)?"-1":i);*/
    }

}