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>
using namespace std;
using ll = long long;
const int MOD = 1e9+7;

int main(){
  
  int k; cin>>k;
  int ans=1;
  ll i = 7, x = 7;
  if(k%2==0||k%5==0){
    cout << -1 << endl;
    return 0;
  }
  x %= k;
  while(1){
    if(x == 0){
      cout << ans << endl;
      return 0;
    }
    i *= 10;
    i %= k;
    x += i;
    x %= k;
    ans++;
  }
}