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

typedef long long ll;
typedef vector<ll> vint;
typedef vector< vector<ll> > vvint;

#define rep(i,n) for(ll i=0;i<n;i++)
#define repf(i,f,n) for(ll i=f;i<n;i++)
#define repr(i,n) for(ll i=n-1;i>=0;i--)
#define mp make_pair
#define mt make_tuple
#define ALL(obj) (obj).begin(), (obj).end()
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

int dy[]={0, 0, 1, -1, 1, -1, -1, 1};
int dx[]={1, -1, 0, 0, 1, 1, -1, -1};


int main() {
    cout<<fixed<<setprecision(10);

    ll k; cin>>k;

    vector<bool> v(k,false);
    ll m = 0;
    ll ans = 1;

    while(true){
        m = (m*10 + 7)%k;
        if(m==0){
            cout<<ans<<endl;
            return 0;
        }
        if(v[m])break;
        v[m] = true;
        ans++;
    }


    cout<<-1<<endl;

    return 0;

}