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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>
#include<algorithm>
#include<unordered_map>

using namespace std;

int main(){
    int k; cin>>k;
    if(k % 2 == 0){
        cout<<-1<<endl;
        return 0;
    }
    long long mod = k * (1e9 + 7);
    long long num = 7;
    for(int i = 1; i <= k; i++){
        if(num % k == 0){
            cout<<i<<endl;
            return 0;
        }
        num = (num * 10 + 7) % mod;
    }
    cout<<-1<<endl;
}