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 IOS ios::sync_with_stdio(false); cin.tie(0);
#define st first
#define nd second
#define endl '\n'
#define what_is(x) cerr << #x << " is " << x << endl;
#define what_is_v(x) cerr << #x << " is "; for(auto&e: (x)) cerr << e << ' '; cerr << '\n'; //vector, set
#define what_is_a(x, n) cerr << #x << " is "; for(int i=0;i<n;i++) cerr << x[i] << ' '; cerr <<  '\n'; //n first element of array
#define cerr_pair(x) '{' << x.st << ", " << x.nd << '}'
#define pwhat_is(x) cerr << #x << " is " << cerr_pair(x) << endl;
#define pwhat_is_v(x) cerr << #x << " is "; for(auto&e: (x)) cerr << cerr_pair(e) << ' '; cerr << '\n'; //vector, set
#define pwhat_is_a(x, n) cerr << #x << " is "; for(int i=0;i<n;i++) cerr << cerr_pair(x[i]) << ' '; cerr <<  '\n'; //n first element of array
// #define int long long
// #define pow mypow

typedef pair<int,int> pii;
const int N = 1e5+5;
const int INF = 1e9+5;
const int MOD = 1e9+7;

int k;
int32_t main()
{
	IOS
	// freopen("input.txt", "r", stdin);
	cin >> k;
	if (k%7 == 0) k /=7;
	int ans = 1;
	int r = 1 % k;
	while(r != 0) {
		r = (10*r + 1) % k;
		ans++;
	}
	cout << ans << endl;
	
	return 0;
}