Problem p02550 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define codefor                                                                \\
  int test;                                                                    \\
  scanf("%d", &test);                                                          \\
  while (test--)
#define INT(...)                                                               \\
  int __VA_ARGS__;                                                             \\
  in(__VA_ARGS__)
#define LL(...)                                                                \\
  ll __VA_ARGS__;                                                              \\
  in(__VA_ARGS__)
#define yn(ans)                                                                \\
  if (ans)                                                                     \\
    printf("Yes\\n");                                                           \\
  else                                                                         \\
    printf("No\\n")
#define YN(ans)                                                                \\
  if (ans)                                                                     \\
    printf("YES\\n");                                                           \\
  else                                                                         \\
    printf("NO\\n")
#define vector1d(type, name, ...) vector<type> name(__VA_ARGS__)
#define vector2d(type, name, h, ...)                                           \\
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define umap unordered_map
#define uset unordered_set
using namespace std;
using ll = long long;
const int MOD = 1000000007;
// 入力系
void scan(int &a) { scanf("%d", &a); }
void scan(long long &a) { scanf("%lld", &a); }
template <class T> void scan(T &a) { cin >> a; }
template <class T> void scan(vector<T> &vec) {
  for (auto &&it : vec)
    scan(it);
}
void in() {}
template <class Head, class... Tail> void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
// 出力系
void print(const int &a) { printf("%d", a); }
void print(const long long &a) { printf("%lld", a); }
void print(const double &a) { printf("%.15lf", a); }
template <class T> void print(const T &a) { cout << a; }
template <class T> void print(const vector<T> &vec) {
  if (vec.empty())
    return;
  print(vec[0]);
  for (auto it = vec.begin(); ++it != vec.end();) {
    putchar(' ');
    print(*it);
  }
}
void out() { putchar('\\n'); }
template <class T> void out(const T &t) {
  print(t);
  putchar('\\n');
}
template <class Head, class... Tail>
void out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
}
// デバッグ系
template <class T> void dprint(const T &a) { cerr << a; }
template <class T> void dprint(const vector<T> &vec) {
  if (vec.empty())
    return;
  cerr << vec[0];
  for (auto it = vec.begin(); ++it != vec.end();) {
    cerr << " " << *it;
  }
}
void debug() { cerr << endl; }
template <class T> void debug(const T &t) {
  dprint(t);
  cerr << endl;
}
template <class Head, class... Tail>
void debug(const Head &head, const Tail &...tail) {
  dprint(head);
  cerr << " ";
  debug(tail...);
}
ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
ll modpow(ll a, ll b, ll p) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
ll updivide(ll a, ll b) {
  if (b == 1)
    return a;
  else if (a % b == 0)
    return a / b;
  else
    return (a / b) + 1;
}

int main() {
  LL(n, x, m);
  ll ans = 0;
  if (n <= 10000000) {
    for (int i = 0; i < n; i++) {
      ans += x;
      x = (x * x) % m;
    }
    out(ans);
  } else {
    vector<ll> syuuki;
    umap<ll, ll> Map;
    ll cycle, T, kaisuu, made;
    for (int i = 0; i < n; i++) {
      if (!Map.count(x)) {
        syuuki.push_back(x);
        Map[x] = i;
        x = (x * x) % m;
      } else {
        cycle = x;
        break;
      }
    }
    ll start = Map[cycle];
    n -= start;
    for (int i = 0; i < start; i++) {
      ans += syuuki[i];
    }
    T = syuuki.size() - Map[cycle];
    kaisuu = n / T;
    made = n % T + start;
    for (int i = start; i < syuuki.size(); i++) {
      ans += ((i < made) + kaisuu) * syuuki[i];
    }
    out(ans);
  }
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define codefor                                                                \\
  int test;                                                                    \\
  scanf("%d", &test);                                                          \\
  while (test--)
#define INT(...)                                                               \\
  int __VA_ARGS__;                                                             \\
  in(__VA_ARGS__)
#define LL(...)                                                                \\
  ll __VA_ARGS__;                                                              \\
  in(__VA_ARGS__)
#define yn(ans)                                                                \\
  if (ans)                                                                     \\
    printf("Yes\\n");                                                           \\
  else                                                                         \\
    printf("No\\n")
#define YN(ans)                                                                \\
  if (ans)                                                                     \\
    printf("YES\\n");                                                           \\
  else                                                                         \\
    printf("NO\\n")
#define vector1d(type, name, ...) vector<type> name(__VA_ARGS__)
#define vector2d(type, name, h, ...)                                           \\
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define umap unordered_map
#define uset unordered_set
using namespace std;
using ll = long long;
const int MOD = 1000000007;
// 入力系
void scan(int &a) { scanf("%d", &a); }
void scan(long long &a) { scanf("%lld", &a); }
template <class T> void scan(T &a) { cin >> a; }
template <class T> void scan(vector<T> &vec) {
  for (auto &&it : vec)
    scan(it);
}
void in() {}
template <class Head, class... Tail> void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
// 出力系
void print(const int &a) { printf("%d", a); }
void print(const long long &a) { printf("%lld", a); }
void print(const double &a) { printf("%.15lf", a); }
template <class T> void print(const T &a) { cout << a; }
template <class T> void print(const vector<T> &vec) {
  if (vec.empty())
    return;
  print(vec[0]);
  for (auto it = vec.begin(); ++it != vec.end();) {
    putchar(' ');
    print(*it);
  }
}
void out() { putchar('\\n'); }
template <class T> void out(const T &t) {
  print(t);
  putchar('\\n');
}
template <class Head, class... Tail>
void out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
}
// デバッグ系
template <class T> void dprint(const T &a) { cerr << a; }
template <class T> void dprint(const vector<T> &vec) {
  if (vec.empty())
    return;
  cerr << vec[0];
  for (auto it = vec.begin(); ++it != vec.end();) {
    cerr << " " << *it;
  }
}
void debug() { cerr << endl; }
template <class T> void debug(const T &t) {
  dprint(t);
  cerr << endl;
}
template <class Head, class... Tail>
void debug(const Head &head, const Tail &...tail) {
  dprint(head);
  cerr << " ";
  debug(tail...);
}
ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
ll modpow(ll a, ll b, ll p) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
ll updivide(ll a, ll b) {
  if (b == 1)
    return a;
  else if (a % b == 0)
    return a / b;
  else
    return (a / b) + 1;
}

int main() {
  LL(n, x, m);
  ll ans = 0;
  if (n <= 10000000) {
    for (int i = 0; i < n; i++) {
      ans += x;
      x = (x * x) % m;
    }
    out(ans);
  } else {
    vector<ll> syuuki;
    set<ll> kind;
    map<ll, ll> Map;
    ll cycle, T, kaisuu, made;
    for (int i = 0; i < n; i++) {
      if (!kind.count(x)) {
        syuuki.push_back(x);
        Map[x] = i;
        x = (x * x) % m;
      } else {
        cycle = x;
        break;
      }
    }
    ll start = Map[cycle];
    n -= start;
    for (int i = 0; i < start; i++) {
      ans += syuuki[i];
    }
    T = syuuki.size() - Map[cycle];
    kaisuu = n / T;
    made = n % T + start;
    for (int i = start; i < syuuki.size(); i++) {
      ans += ((i < made) + kaisuu) * syuuki[i];
    }
    out(ans);
  }
}