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)

// https://atcoder.jp/contests/abc175/tasks/abc175_c
#include <iostream>
#include <vector>
#include <deque>
#include <tuple>
#include <algorithm>
#include <iterator> // std::back_inserter
#include <climits>
#include <sstream>

using namespace std;

typedef unsigned long ll;

ll k;
ll a[1000001];

int main()
{
    cin >> k;
    ll x = 7;
    for (int i=0; i<k; i++) {
        if (x % k == 0) {
            cout << i+1 << endl;
            return 0;
        }
        x = (x * 10 + 7) % k;
    }
    cout << -1 << endl;
}