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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define pb push_back
#define pr pair<int,int>
#define PI 3.1415926535897932384626
#define mod 1000000007
#define fo(i,n) for(i=0;i<n;i++)
#define endl "\n"
#define mset(m,v) memset(m,v,sizeof(m))
typedef vector<int>	vi;

void solve()
{
	int n,i=1,x=0;
	cin >> n ;
	if(n%2==0){
	    cout << -1;
	    return ;
	}
	while(i++){
	    x+=7;
	    x%=n;
	    if(x==0){
	        cout << i-1;
	        return ;
	    }
	    x*=10;
	}
	cout << endl;
}

int32_t main()
{
	ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL);
	int t=1;//cin>>t;
	for(int i=1;i<=t;i++){	solve();}
	return 0;
}