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: Wrong Answer)

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

#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vll vector<ll>
#define vpii vector<pair<int,int>>
#define vpll vector<pair<ll,ll>>
#define fr(i,k,n) for (int i = k; i < n; ++i)
#define fri(i,k,n) for (int i = k; i >= n; --i)
#define INF (int)1e9
#define MOD 1000000007
#define pb push_back
#define mp make_pair
#define all(arr) arr.begin(),arr.end()

void boost(){
	ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

int gcd(int a, int b) 
{ 
    if (b == 0) 
        return a; 
    return gcd(b, a % b);  
      
} 

ll phi(ll n) {
    ll result = n;
    for (ll i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            while (n % i == 0)
                n /= i;
            result -= result / i;
        }
    }
    if (n > 1)
        result -= result / n;
    return result;
}

inline ll exp(ll x, ll n, ll m = MOD) {
    ll r = 1;
    while(n) {
        if(n & 1) r = r * x % m;
        x = x * x % m, n >>= 1;
    }
    return r;
}

void solve(){
	int k;
	cin>>k;
	if(gcd(9,k)!=1 || gcd(7,k)!=1 || gcd(10,k)!=1){
		cout<<-1<<endl;
		return;
	}
	ll temp=phi(k);
	int ans=-1;
	for(int i=1;i<=temp;i++){
		if(exp(10,i,k)%k==1){
			ans=i;
			break;
		}
	}
	cout<<ans<<endl;
	return;
}

int main()
{
	boost();
	
	int tc=1;
	//cin>>tc;
	while(tc--)
		solve();
	return 0;
}