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++ (Clang 10.0.0) (judge verdict: Accepted)

#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <cmath>
#include <numeric>
#include <utility>
#include <iomanip>

using namespace std;
using int64 = long long;

struct aaa{aaa(){cin.tie(nullptr); ios::sync_with_stdio(false); cout<<fixed<<setprecision(20);};}aaa;

int main() {
    int k;
    cin >> k;
    vector<bool> check(k, false);
    int ans = 1;
    int seven = 7;
    for (int i=0; i<k; i++) {
        if (seven%k == 0)
            break;
        if (check[seven%k]) {
            ans = -1;
            break;
        }
        check[seven%k] = true;
        seven = seven*10 + 7;
        seven %= k;
        ans++;
    }
    cout << ans << endl;
}