//* #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") //*/ // #include #include using namespace std; // using namespace atcoder; // #define _GLIBCXX_DEBUG #define DEBUG(x) cerr << #x << ": " << x << endl; #define DEBUG_VEC(v) \ cerr << #v << ":"; \ for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \ cerr << " " << v[iiiiiiii]; \ cerr << endl; #define DEBUG_MAT(v) \ cerr << #v << endl; \ for (int iv = 0; iv < v.size(); iv++) { \ for (int jv = 0; jv < v[iv].size(); jv++) { \ cerr << v[iv][jv] << " "; \ } \ cerr << endl; \ } typedef long long ll; // #define int ll #define vi vector #define vl vector #define vii vector> #define vll vector> #define vs vector #define pii pair #define pis pair #define psi pair #define pll pair template pair operator+(const pair &s, const pair &t) { return pair(s.first + t.first, s.second + t.second); } template pair operator-(const pair &s, const pair &t) { return pair(s.first - t.first, s.second - t.second); } template ostream &operator<<(ostream &os, pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define X first #define Y second #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rrep1(i, n) for (int i = (int)(n); i > 0; i--) #define REP(i, a, b) for (int i = a; i < b; i++) #define in(x, a, b) (a <= x && x < b) #define all(c) c.begin(), c.end() void YES(bool t = true) { cout << (t ? "YES" : "NO") << endl; } void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; } void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; } void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; } void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; } void no(bool t = true) { cout << (t ? "no" : "yes") << endl; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const long double pi = 3.1415926535897932384626433832795028841971L; int popcount(ll t) { return __builtin_popcountll(t); } // int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 }; vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0}; vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1}; struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(25); } } setup_io; // const ll MOD = 1000000007; const ll MOD = 998244353; // #define mp make_pair //#define endl '\n' int just_win(ll n, ll x, ll y, ll p) { ll non_las; non_las = n / 2; if (min(x, y) <= non_las) { ll ret = inf; if (x <= non_las) { if ((n - x) % 2 == 1) { ret = -1; } else { ret = 1; } } if (y <= non_las) { if (y % 2 == 0) { ret = 1; } else { ret = -1; } } assert(ret != inf); if (ret == p) { return 1; } else { return -1; } } if (n % 2 == 0) { return -1; } return 0; } bool solve(ll x, ll y, ll k, ll p) { ll n = x + y - k; if (y % 2 == 1) { p *= -1; } int jw = just_win(n, x, y, p); if (jw != 0) { if (jw == 1) { return true; } else { return false; } return 0; } assert(n % 2 == 1); int p1 = just_win(n - 1, x - 1, y, p); int p2 = just_win(n - 1, x, y - 1, -p); if (p1 == -1 or p2 == -1) { return true; } else { return false; } } bool guchoku(ll x, ll y, ll k, ll p) { ll n = x + y + k; chmax(p, 0LL); vector> dp(n + 1, vector(x + 1, vii(y + 1, vi(2)))); rep(i, x + 1) { rep(j, y + 1) { dp[n][i][j][p] = 1; dp[n][i][j][1 - p] = 0; } } for (int i = n - 1; i >= 0; i--) { rep(j, x + 1) { rep(k, y + 1) { rep(l, 2) { vi to; if (j > 0) { int nj = j - 1; int nk = k; int nl = l; to.push_back(dp[i + 1][nj][nk][nl]); } if (k > 0) { int nj = j; int nk = k - 1; int nl = 1 - l; to.push_back(dp[i + 1][nj][nk][nl]); } if (to.size() == 0) { continue; } sort(all(to)); if (i % 2 == 0) { if (to.back() == 1) { dp[i][j][k][l] = 1; } else { dp[i][j][k][l] = 0; } } else { if (to[0] == 0) { dp[i][j][k][l] = 0; } else { dp[i][j][k][l] = 1; } } DEBUG(dp[i][j][k][l]); } } } } return dp[0][x][y][1] == 1; } signed main() { ll x, y, k, p; cin >> x >> y >> k >> p; bool so = solve(x, y, k, p); // bool gu = guchoku(x, y, k, p); // DEBUG(pii(so, gu)); // assert(so == gu); if (so) { cout << "Alice" << endl; } else { cout << "Bob" << endl; } }