https://atcoder.jp/contests/abc255/tasks/abc255_g

// compile: g++ -o data data.cpp -O3 -std=gnu++20 -Wall -Wextra -Wshadow -D_GLIBCXX_ASSERTIONS -ggdb3 -fmax-errors=2 -DLOCAL
// run: ./data < data.in
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) {_variables(#x);_print(x);}
#else
#define debug(x...)
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define INTMAX (int)(9223372036854775807)
#define INTINF (int)(1152921504606846976)
#define int long long
#define MAXN 200010
 
int n, m;
vector<int> a;
struct node {
    int s, minus, g;
    vector<int> ban;
};
vector<node> f;
map<int, int> cnt;
 
int binary_search(vector<node> &a, int l, int r, int x) {
    int ans = -1;
    while (l <= r) {
        int mid = l + (r-l) / 2;
        if (a[mid].s > x) r = mid - 1;
        else ans = mid, l = mid + 1;
    }
    return ans;
}
 
int sg(int x) {
    int ind = binary_search(f, 0, sz(f)-1, x);
    if (!~ind) return x;
    if (f[ind].s == x) return f[ind].g;
    return x - f[ind].minus;
}
 
void init() {
    int num = 0, maxsg = f[0].s - 1;
    rep(i, 0, sz(f)) {
        int minv = INTINF;
        map<int, int> v;
        for (auto j: f[i].ban) {
            int t = sg(f[i].s - j);
            ++v[t];
        }
        for (auto [key, value]: v) {
            if (cnt[key] + 1 == value) {
                minv = key;
                break;
            }
        }
        if (minv != INTINF) {
            ++cnt[minv];
            f[i].g = minv;
            f[i].minus = ++num;
        }
        else {
            f[i].g = ++maxsg;
            f[i].minus = num;
        }
        if (i+1 < sz(f) && f[i+1].s > f[i].s+1) maxsg = max(maxsg, f[i+1].s - f[i].minus - 1);
    }
}
 
int32_t main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
 
    cin >> n >> m; a.resize(n);
    rep(i, 0, n) cin >> a[i];
    vector<pair<int, int>> t(m);
    rep(i, 0, m) cin >> t[i].first >> t[i].second;
    sort(t.begin(), t.end());
    f.push_back({t[0].first, 0, 0, {t[0].second}});
    rep(i, 1, m) {
        if (t[i].first != t[i-1].first) f.push_back({t[i].first, 0, 0, {}});
        f.rbegin()->ban.push_back(t[i].second);
    }
    init();
    int ans = 0;
    rep(i, 0, n) ans ^= sg(a[i]);
    cout << (ans ? "Takahashi" : "Aoki") << endl;
 
    return 0;
}