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)

#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")

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

#define v vector
#define ALL(x) x.begin(),x.end()
#define rALL(x) x.rbegin(),x.rend()
#define endl '\n'
#define F first
#define S second
#define DEBUG

template<typename T> void DBG(const char* name, T&& H) {
	cerr << name << " = " << H << ')' << endl;
}

template<typename T, typename... Args> void DBG(const char* names, T&& H, Args&&... args) {
	const char* NEXT = strchr(names+1, ',');
	cerr.write(names, NEXT-names) << " = " << H << " |";
	DBG(NEXT+1, args...);
}

#ifdef DEBUG
	#define dbg(...) cerr << __FUNCTION__ << ' ' <<__LINE__ << " : (", DBG(#__VA_ARGS__, __VA_ARGS__)
#else
	#define dbg(...)
#endif

using ll = long long;
using ld = long double;

const long long mod = 998244353;
const long double PI = acos(-1.0);
const long long INF = 1e18;
const int maxN = 2e5+1;

void Solve() {
	int K;
	cin >> K;
	vector<int> seven(1e6+100);
	seven[0] = 0;
	seven[1] = 7 % K;
	for(int i = 2; i < seven.size(); i ++) {
		seven[i] = (seven[i-1] * 10) % K;
	}
	for(int i = 2; i < seven.size(); i ++) {
		seven[i] = (seven[i]+seven[i-1]) % K;
	}
	int idx = -1;
	for(int i = 1; i <= seven.size()-1; i ++) {
		if(seven[i] == 0) {
			idx = i;
			break;
		}
	} 
	cout << idx << endl;
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	int tt = 1;
	while(tt --) {
		Solve();
	}
	
	return 0;
}