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: Wrong Answer)



#include <bits/stdc++.h>

#define loop(s, e, i) for (int i = s; i < e; ++i)
#define print(s) cout << s << endl;
#define DIV 1000000007
using namespace std;
using ll = long long;
using lld = long long;

/*
浮動小数点の入力
cout << fixed << setprecision(9) << endl;
*/

ll gcd(ll a, ll b)
{
  if (a < b)
  {
    return gcd(b, a);
  }
  while (b != 0)
  {
    ll tmp = b;
    b = a % b;
    a = tmp;
  }
  return a;
}

ll modinv(ll a, ll m) {
  ll b = m, u = 1, v = 0;
  while(b) {
    ll t =  a / b;
    a -= t * b; swap(a, b);
    u -= t * v; swap(u, v);
  }
  u %= m;
  if (u < 0) u += m;
  return u;
}

int bit_counter(int x) {
  if (x == 0) return 0;
  return bit_counter(x >> 1) + (x&1);
}

int main() {
  ll K;
  cin >> K;

  vector<int> A(K+1);
  A[0] = 7%K;
  loop(1, K+1, i) {
    A[i] = (10 * A[i-1] + 7)%K;
  }
  loop(0, K+1, i) {
    if (A[i] == 0) {
      print(i+1);
      break;
    }
  }
}