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)

// NK
#include <bits/stdc++.h>
using namespace std;

typedef pair<int,int> ii;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<ll> vll;
#define pb push_back
#define eb emplace_back
#define pob pop_back
#define psf push_front
#define pof pop_front
#define mkp make_pair
#define mkt make_tuple
#define all(x) x.begin(), x.end()

int main(){
	ios::sync_with_stdio(false), cin.tie(nullptr);
    
    ll k; cin>>k;
    if (k == 1){
        cout<<k<<'\n';
        return 0;
    }
    ll c = 7;
    ll curr = 0;
    ll pw = 1;
    for (ll i=1; i<=k; i++){
        curr += c * pw;
        curr %= k;
        if (curr == 0){
            cout<<i<<'\n';
            return 0;
        }
        pw *= (ll)10;
        pw %= k;
    }
    cout<<-1<<'\n';
	return 0;
}
/*
NARCO
*/