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>

#define mp make_pair
#define ff first
#define ss second
#define pii pair <int,int>
#define pb push_back
#define debug(x)  cerr << #x << " = " << x << endl
using namespace std ;
typedef long long ll ;
const int mx = 1000005 ;
bool mark[mx] ;


int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int k, node, x=1 ;
	cin >> k ;
	node = (7%k) ;
	mark[node] =1 ;
	if(node == 0){
		cout << x ;
		return 0 ;
	}
	while(1){
		x++ ;
		int nodex = (node*10+7)%k ;
//		cout << node << ' ' << nodex << ' ' << mark[nodex] <<'\n' ;
		if(mark[nodex]){
			break ;
		}
		if(nodex == 0){
			mark[nodex] = 1 ;
			break ;
		}
		mark[nodex] = 1 ;
		node = nodex ;
	}
	if(mark[0] == 1){
		cout << x ;
	}
	else{
		cout << -1 << '\n' ;
	}
	
	return 0 ;
}