Problem p03422 (C++)

Buggy submission (status: Time Limit Exceeded):
// #define DEBUGGING
#include <bits/stdc++.h>
#define endl '\n'
#define ALL(V) (V).begin(), (V).end()
#define ALLR(V) (V).rbegin(), (V).rend()
template <typename T> using V = std::vector<T>;
template <typename T> using VV = V<V<T>>;
using ll = std::int64_t;
using ull = std::uint64_t;
using PLL = std::pair<ll, ll>;
using TLL = std::tuple<ll, ll, ll>;
template <typename T> const T &var_min(const T &t) { return t; }
template <typename T> const T &var_max(const T &t) { return t; }
template <typename T, typename... Tail>
const T &var_min(const T &t, const Tail &...tail) {
  return std::min(t, var_min(tail...));
}
template <typename T, typename... Tail>
const T &var_max(const T &t, const Tail &...tail) {
  return std::max(t, var_max(tail...));
}
template <typename T, typename... Tail> void chmin(T &t, const Tail &...tail) {
  t = var_min(t, tail...);
}
template <typename T, typename... Tail> void chmax(T &t, const Tail &...tail) {
  t = var_max(t, tail...);
}
template <typename T> const T &clamp(const T &t, const T &low, const T &high) {
  return std::max(low, std::min(high, t));
}
template <typename T> void chclamp(T &t, const T &low, const T &high) {
  return t = clamp(t, low, high);
}
namespace init__ {
struct InitIO {
  InitIO() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(30);
  }
} init_io;
} // namespace init__
#define mv_rec make_v(init, tail...)
template <typename T> T make_v(T init) { return init; }
template <typename T, typename... Tail>
auto make_v(T init, size_t s, Tail... tail) {
  return V<decltype(mv_rec)>(s, mv_rec);
}
#undef mv_rec
using namespace std;
#ifdef DEBUGGING
#include "../../debug/debug.cpp"
#else
#define DEBUG(...) 0
#define DEBUG_SEPARATOR_LINE 0
#endif

int main() {
  ll N;
  cin >> N;
  V<PLL> ak(N);
  for (auto &&ele : ak) {
    ll a, b;
    cin >> a >> b;
    ele = PLL(a, b);
  }
  ll sum = 0;
  for (auto &&ele : ak) {
    ll a, k;
    tie(a, k) = ele;
    while (a % k && k <= a) {
      ll dec = a / k + 1;
      if (a < dec)
        break;
      a -= dec;
    }
    sum ^= a / k;
  }
  cout << (sum ? "Takahashi" : "Aoki") << endl;
  return 0;
}


Fixed submission:
// #define DEBUGGING
#include <bits/stdc++.h>
#define endl '\n'
#define ALL(V) (V).begin(), (V).end()
#define ALLR(V) (V).rbegin(), (V).rend()
template <typename T> using V = std::vector<T>;
template <typename T> using VV = V<V<T>>;
using ll = std::int64_t;
using ull = std::uint64_t;
using PLL = std::pair<ll, ll>;
using TLL = std::tuple<ll, ll, ll>;
template <typename T> const T &var_min(const T &t) { return t; }
template <typename T> const T &var_max(const T &t) { return t; }
template <typename T, typename... Tail>
const T &var_min(const T &t, const Tail &...tail) {
  return std::min(t, var_min(tail...));
}
template <typename T, typename... Tail>
const T &var_max(const T &t, const Tail &...tail) {
  return std::max(t, var_max(tail...));
}
template <typename T, typename... Tail> void chmin(T &t, const Tail &...tail) {
  t = var_min(t, tail...);
}
template <typename T, typename... Tail> void chmax(T &t, const Tail &...tail) {
  t = var_max(t, tail...);
}
template <typename T> const T &clamp(const T &t, const T &low, const T &high) {
  return std::max(low, std::min(high, t));
}
template <typename T> void chclamp(T &t, const T &low, const T &high) {
  return t = clamp(t, low, high);
}
namespace init__ {
struct InitIO {
  InitIO() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(30);
  }
} init_io;
} // namespace init__
#define mv_rec make_v(init, tail...)
template <typename T> T make_v(T init) { return init; }
template <typename T, typename... Tail>
auto make_v(T init, size_t s, Tail... tail) {
  return V<decltype(mv_rec)>(s, mv_rec);
}
#undef mv_rec
using namespace std;
#ifdef DEBUGGING
#include "../../debug/debug.cpp"
#else
#define DEBUG(...) 0
#define DEBUG_SEPARATOR_LINE 0
#endif

int main() {
  ll N;
  cin >> N;
  V<PLL> ak(N);
  for (auto &&ele : ak) {
    ll a, b;
    cin >> a >> b;
    ele = PLL(a, b);
  }
  ll sum = 0;
  for (auto &&ele : ak) {
    ll a, k;
    tie(a, k) = ele;
    while (a % k && k <= a) {
      ll dec = a / k + 1;
      if (a < dec)
        break;
      ll aim = a / k * k;
      ll diff = a - aim;
      ll cnt = diff / dec + !!(diff % dec);
      a -= dec * cnt;
    }
    sum ^= a / k;
  }
  cout << (sum ? "Takahashi" : "Aoki") << endl;
  return 0;
}