Problem p03422 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, -1, 0, 1};
const char dir[4] = {'u', 'l', 'd', 'r'};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw) (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)
#pragma warning(disable : 4996)

int n;
LL a[202], k[202];

LL calc(LL a, LL k) {
  if (a < k)
    return 0;
  if (a % k == 0)
    return a / k;

  return calc(a - (a / k) - 1, k);
}

int main() {
  cin >> n;
  LL g = 0;
  REP(i, n) {
    cin >> a[i] >> k[i];
    g ^= calc(a[i], k[i]);
  }
  cout << (g > 0 ? "Takahashi" : "Aoki") << endl;
}

Fixed submission:
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, -1, 0, 1};
const char dir[4] = {'u', 'l', 'd', 'r'};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw) (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)
#pragma warning(disable : 4996)

int n;
LL a[202], k[202];

LL calc(LL a, LL k) {
  if (a < k)
    return 0;
  if (a % k == 0)
    return a / k;

  LL dif = ((a / k) + 1);
  return calc(a - max((a % k) / dif, 1LL) * dif, k);
}

int main() {
  cin >> n;
  LL g = 0;
  REP(i, n) {
    cin >> a[i] >> k[i];
    g ^= calc(a[i], k[i]);
  }
  cout << (g > 0 ? "Takahashi" : "Aoki") << endl;
}