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;

int main() {
  int K;
  cin >> K;
  
  if (K % 2 == 0) cout << -1 << endl;
  else {
    int64_t sevens = 0;
    for (int i = 1; i <= 1e7; i++) {
      sevens = (10 * sevens + 7) % K;  // ここでmod Kしてしまえばオーバーフローを防げる
      if (sevens == 0) {
        cout << i << endl;
        // breakだとforスコープのみ抜けるが, return 0とすればelseスコープを抜ける
        // というかreturn以降の処理は実行されない
        return 0;
      }
    }
    cout << -1 << endl;  // 上限値までループしても見つからなかった場合
  }
}