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
void solve(){
    int k;cin>>k;
	if(k%2==0) {cout<<-1;return;}
    string s="7";
    int last=0;
    bool no=true;
    for(int i=1;i<=1e6;i++){
        int curr=((last*(10%k))%k+(7%k))%k;
        if(curr%k==0) {cout<<i;no=false;
        break;}
        last=curr;
        s=s+"7";
    }
    if(no) cout<<-1;
}
int32_t main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);cout.tie(NULL); 
	int T=1;
	// cin>>T;
	while(T--){
		solve();
	}
	return 0;
}