Problem p03422 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <bitset>
#include <cstdio>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <string.h>
#include <string>
#define REP(i, a, n) for (int i = a; i <= n; ++i)
#define PER(i, a, n) for (int i = n; i >= a; --i)
#define hr putchar(10)
#define pb push_back
#define lc (o << 1)
#define rc (lc | 1)
#define mid ((l + r) >> 1)
#define ls lc, l, mid
#define rs rc, mid + 1, r
#define x first
#define y second
#define io std::ios::sync_with_stdio(false)
#define endl '\n'
#define DB(a)                                                                  \
  ({                                                                           \
    REP(__i, 1, n) cout << a[__i] << ' ';                                      \
    hr;                                                                        \
  })
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int P = 1e9 + 7, INF = 0x3f3f3f3f;
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll qpow(ll a, ll n) {
  ll r = 1 % P;
  for (a %= P; n; a = a * a % P, n >>= 1)
    if (n & 1)
      r = r * a % P;
  return r;
}
ll inv(ll x) { return x <= 1 ? 1 : inv(P % x) * (P - P / x) % P; }
inline int rd() {
  int x = 0;
  char p = getchar();
  while (p < '0' || p > '9')
    p = getchar();
  while (p >= '0' && p <= '9')
    x = x * 10 + p - '0', p = getchar();
  return x;
}
// head

int sg(int x, int k) {
  if (k > x)
    return 0;
  if (x % k == 0)
    return x / k;
  int a = x / k - 1, b = x % k;
  if (a >= b)
    return sg(x - a, k);
  return sg(x - b / a * a, k);
}

int main() {
  int n;
  scanf("%d", &n);
  int ans = 0;
  REP(i, 1, n) {
    int a, k;
    scanf("%d%d", &a, &k);
    ans ^= sg(a, k);
  }
  puts(ans ? "Takahashi" : "Aoki");
}


Fixed submission:
#include <algorithm>
#include <bitset>
#include <cstdio>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <string.h>
#include <string>
#define REP(i, a, n) for (int i = a; i <= n; ++i)
#define PER(i, a, n) for (int i = n; i >= a; --i)
#define hr putchar(10)
#define pb push_back
#define lc (o << 1)
#define rc (lc | 1)
#define mid ((l + r) >> 1)
#define ls lc, l, mid
#define rs rc, mid + 1, r
#define x first
#define y second
#define io std::ios::sync_with_stdio(false)
#define endl '\n'
#define DB(a)                                                                  \
  ({                                                                           \
    REP(__i, 1, n) cout << a[__i] << ' ';                                      \
    hr;                                                                        \
  })
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int P = 1e9 + 7, INF = 0x3f3f3f3f;
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll qpow(ll a, ll n) {
  ll r = 1 % P;
  for (a %= P; n; a = a * a % P, n >>= 1)
    if (n & 1)
      r = r * a % P;
  return r;
}
ll inv(ll x) { return x <= 1 ? 1 : inv(P % x) * (P - P / x) % P; }
inline int rd() {
  int x = 0;
  char p = getchar();
  while (p < '0' || p > '9')
    p = getchar();
  while (p >= '0' && p <= '9')
    x = x * 10 + p - '0', p = getchar();
  return x;
}
// head

int sg(int x, int k) {
  if (k > x)
    return 0;
  if (x % k == 0)
    return x / k;
  int a = x / k + 1, b = x % k;
  return sg(x - (b + a - 1) / a * a, k);
}

int main() {
  int n;
  scanf("%d", &n);
  int ans = 0;
  REP(i, 1, n) {
    int a, k;
    scanf("%d%d", &a, &k);
    ans ^= sg(a, k);
  }
  puts(ans ? "Takahashi" : "Aoki");
}