Problem p02596 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(vector<vector<T>> x) {
  cerr << "\\n{";
  int f = x.size();
  for (int i = 0; i < f; i++) {
    cerr << "(";
    int g = x[i].size();
    for (auto j : x[i]) {
      cerr << j;
      (--g != 0) ? cerr << "," : cerr << "";
    }
    cerr << ")\\n";
  }
  cerr << "}";
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void __print(vector<bool> x) {
  cerr << "{";
  int f = x.size();
  for (auto i : x) {
    cerr << i;
    (--f != 0) ? cerr << "," : cerr << "";
  }
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}

#ifndef ONLINE_JUDGE
#define trace(x...) cerr << "[" << #x << "] = [", _print(x)
#else
#define trace(x...)
#endif

template <typename... T> void read(T &...args) { ((cin >> args), ...); }

template <typename... T> void writ(T &&...args) {
  ((cout << args << " "), ...);
}
#define ull unsigned long long
#define ll long long
#define MOD 1000000007
#define INF (ll)1e18
#define IINF (int)1e9
#define EPS 1e-9
/*
    XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
    In the blazing sun I saw you
    In the shadows hiding from yourself
    When the lights are on I know you
    See you're grey from all the lies you tell
    XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
*/

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll k;
  cin >> k;
  if (k % 5 != 0 && k & 1) {
    ll x = 0; // This is mostly assumption based but I still need to prove it
    bool flag = true;
    ll ans = 0;
    while (flag) { // there is meant to be some condition here I don't know what
      x = ((x * 10) + 7) % k;
      ans++;
      trace(ans, x);
      if (!x)
        flag = false;
    }
    cout << ans << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\\'' << x << '\\''; }
void __print(const char *x) { cerr << '\\"' << x << '\\"'; }
void __print(const string &x) { cerr << '\\"' << x << '\\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }

template <typename T, typename V> void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T> void __print(vector<vector<T>> x) {
  cerr << "\\n{";
  int f = x.size();
  for (int i = 0; i < f; i++) {
    cerr << "(";
    int g = x[i].size();
    for (auto j : x[i]) {
      cerr << j;
      (--g != 0) ? cerr << "," : cerr << "";
    }
    cerr << ")\\n";
  }
  cerr << "}";
}
template <typename T> void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x)
    cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void __print(vector<bool> x) {
  cerr << "{";
  int f = x.size();
  for (auto i : x) {
    cerr << i;
    (--f != 0) ? cerr << "," : cerr << "";
  }
  cerr << "}";
}
void _print() { cerr << "]\\n"; }
template <typename T, typename... V> void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v))
    cerr << ", ";
  _print(v...);
}

#ifndef ONLINE_JUDGE
#define trace(x...) cerr << "[" << #x << "] = [", _print(x)
#else
#define trace(x...)
#endif

template <typename... T> void read(T &...args) { ((cin >> args), ...); }

template <typename... T> void writ(T &&...args) {
  ((cout << args << " "), ...);
}
#define ull unsigned long long
#define ll long long
#define MOD 1000000007
#define INF (ll)1e18
#define IINF (int)1e9
#define EPS 1e-9
/*
    XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
    In the blazing sun I saw you
    In the shadows hiding from yourself
    When the lights are on I know you
    See you're grey from all the lies you tell
    XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
*/

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ll k;
  cin >> k;
  if (k & 1) {
    ll x = 0; // This is mostly assumption based but I still need to prove it
    bool flag = true;
    ll ans = 0;
    while (flag) { // there is meant to be some condition here I don't know what
      x = ((x * 10) + 7) % k;
      ans++;
      if (!x)
        flag = false;
    }
    cout << ans << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}