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>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename key>
using ordered_set = tree<key, null_type, less<key>, rb_tree_tag, tree_order_statistics_node_update>;
#define F first
#define S second
#define T second.first
#define C second.second
#define FIO ios_base::sync_with_stdio(0);cin.tie(0);
#define all(v) v.begin(),v.end()
#define OO 0x3f3f3f3fLL
#define INF 0x3f3f3f3f3f3f3f3fLL
#define sz(s) (int)(s.size())
#define RT(s) return cout<<s,0
typedef long long ll;
typedef long double ld;
typedef pair<ll, ll> pii;
typedef pair<ll,pair<ll,ll>> piii;
const int N = 2e5+5, M= 20, mod = 1000000000;
const double EPS = 1e-10;

int main(){
    FIO
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
    ll k;
    cin>>k;
    ll prev = 0;
    bool f = 0;
    for(int i=0; i<k+k; i++){
        ll cur = ((prev*10LL)%k) +7LL;
        cur%=k;
        if(cur == 0){
            cout<<i+1;
            f = 1;
            break;
        }
        prev = cur;
    }
    if(f == 0)RT(-1);
}