Language: C++

//start of jonathanirvings' template v3.0.3 (BETA)

#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef pair<int,int> pii;
typedef pair<LL,LL> pll;
typedef pair<string,string> pss;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pii> vii;
typedef vector<LL> vl;
typedef vector<vl> vvl;

double EPS = 1e-9;
int INF = 1000000005;
long long INFF = 1000000000000000005LL;
double PI = acos(-1);
int dirx[8] = {-1,0,0,1,-1,-1,1,1};
int diry[8] = {0,1,-1,0,-1,1,-1,1};

#ifdef TESTING
  #define DEBUG fprintf(stderr,"====TESTING====\n")
  #define VALUE(x) cerr << "The value of " << #x << " is " << x << endl
  #define debug(...) fprintf(stderr, __VA_ARGS__)
#else
  #define DEBUG 
  #define VALUE(x)
  #define debug(...)
#endif

#define FOR(a,b,c) for (int (a)=(b);(a)<(c);++(a))
#define FORN(a,b,c) for (int (a)=(b);(a)<=(c);++(a))
#define FORD(a,b,c) for (int (a)=(b);(a)>=(c);--(a))
#define FORSQ(a,b,c) for (int (a)=(b);(a)*(a)<=(c);++(a))
#define FORC(a,b,c) for (char (a)=(b);(a)<=(c);++(a))
#define FOREACH(a,b) for (auto &(a) : (b))
#define REP(i,n) FOR(i,0,n)
#define REPN(i,n) FORN(i,1,n)
#define MAX(a,b) a = max(a,b)
#define MIN(a,b) a = min(a,b)
#define SQR(x) ((LL)(x) * (x))
#define RESET(a,b) memset(a,b,sizeof(a))
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ALL(v) v.begin(),v.end()
#define ALLA(arr,sz) arr,arr+sz
#define SIZE(v) (int)v.size()
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define SORTA(arr,sz) sort(ALLA(arr,sz))
#define REVERSEA(arr,sz) reverse(ALLA(arr,sz))
#define PERMUTE next_permutation
#define TC(t) while(t--)

inline string IntToString(LL a){
  char x[100];
  sprintf(x,"%lld",a); string s = x;
  return s;
}

inline LL StringToInt(string a){
  char x[100]; LL res;
  strcpy(x,a.c_str()); sscanf(x,"%lld",&res);
  return res;
}

inline string GetString(void){
  char x[1000005];
  scanf("%s",x); string s = x;
  return s;
}

inline string uppercase(string s){
  int n = SIZE(s); 
  REP(i,n) if (s[i] >= 'a' && s[i] <= 'z') s[i] = s[i] - 'a' + 'A';
  return s;
}

inline string lowercase(string s){
  int n = SIZE(s); 
  REP(i,n) if (s[i] >= 'A' && s[i] <= 'Z') s[i] = s[i] - 'A' + 'a';
  return s;
}

inline void OPEN (string s) {
  #ifndef TESTING
  freopen ((s + ".in").c_str (), "r", stdin);
  freopen ((s + ".out").c_str (), "w", stdout);
  #endif
}

//end of jonathanirvings' template v3.0.3 (BETA)

int dp[1005][1005];
int op;

int nimber(int x,int y)
{
  int &ret = dp[x][y];
  if (ret >= 0) return ret;
  vi tes;
  FORN(i,1,x/y) tes.pb(nimber(x-i,y));
  SORT(tes);
  tes.erase(unique(ALL(tes)),tes.end());
  REP(i,SIZE(tes)) if(tes[i] != i) return ret = i;
  return ret = SIZE(tes);
}

int nimber2(int x,int y)
{
  ++op;
  if (op >= 175000000)
  {
    if (risan > 0) puts("Takahashi");
    else puts("Aoki");
    exit(0);
    return 0;
  }
  if (x < y) return 0;
  if (x % y == 0) return x / y;
  return nimber2(x - x / y - 1, y);
}

int ppp(int x,int y)
{
  if (x % y == 0) return 0;
  return ppp(x - x / y - 1, y) + 1;
}

int n,a,k;
int risan = 0;

int main()
{
  srand(time(NULL));
  // FORN(i,1,30) VALUE(__gcd(i,3));
  // RESET(dp,-1);
  // FORN(j,1,30) FORN(i,1,30)  debug("%d %d: %d\n",i,j,nimber(i,j));
  // FORN(j,1,30)
  // {
  //   FORN(i,1,30) debug("%3d",nimber2(i,j));
  //   debug("\n");
  // }
  // FORN(j,1,30) FORN(i,1,30) 
  // {
  //   debug("%d %d %d %d\n",i,j,nimber(i,j),nimber2(i,j));
  //   assert(nimber(i,j) == nimber2(i,j));
  // }
  // // VALUE(nimber2(INF,2));
  // FORN(i,1,1000) VALUE(nimber2(INF,INF/3+i));
  scanf("%d",&n);
  REP(i,n)
  {
    scanf("%d %d",&a,&k);
    risan ^= nimber2(a,k);
  }
  // printf("%d\n",op);
  puts(risan ? "Takahashi" : "Aoki");
  return 0;
}











Compiler output:
a.cc: In function 'int nimber2(int, int)':
a.cc:118:9: error: 'risan' was not declared in this scope
  118 |     if (risan > 0) puts("Takahashi");
      |         ^~~~~