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 ll long long
    #define ld long double
   ll gcd(ll a,ll b)
   {
    if(b==0)
        return a;
    return gcd(b,a%b);
   }
    int main()
    {
        ll k;
        cin >> k;
        ll mod=9*k;
        if(k%2 == 0 && k%5 == 0)
            cout << "-1\n";
        else
        {
            ll init=70;
            ll cnt=1;
            while(1)
            {
                init=(init*10)%mod;
                cnt++;
            }
            cout << cnt << "\n";
        }
    }