#include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } bool ok[305][305][605][2]; bool win[305][305][605][2]; bool solve(int x, int y, int k, int p){ int pp = p == 1 ? 1 : 0; if(ok[x][y][k][pp]) return win[x][y][k][pp]; if(x+y == k) return p == 1; if(x > 0 && !solve(x-1, y, k, -p)) win[x][y][k][pp] = true; if(y > 0 && !solve(x, y-1, k, p)) win[x][y][k][pp] = true; ok[x][y][k][pp] = true; return win[x][y][k][pp]; } bool solve0(int x, int y, int k, int p){ if(x+y == k) return p == 1; int used = x+y-k; if(used%2 == 0){ // 最後がBob int c = used/2; if(x > c && y > c) return false; if(x <= c){ // 残りk個の-1 int q = (y-k)%2 == 0 ? 1 : -1; if(p == q) return true; } if(y <= c){ int q = y%2 == 0 ? 1 : -1; if(p == q) return true; } return false; }else{ // 最後がAlice if(x > 0 && !solve0(x-1, y, k, -p)) return true; if(y > 0 && !solve0(x, y-1, k, p)) return true; return false; } } void test(int n){ for(int x = 0; x <= n; x++){ for(int y = 0; y <= n; y++){ for(int k = 1; k < x+y; k++){ for(int p: {-1, 1}){ if(solve(x, y, k, p) != solve0(x, y, k, p)) cout << x << ' ' << y << ' ' << k << ' ' << p << ' ' << solve(x, y, k, p) << ' ' << solve0(x, y, k, p) << endl; } } } } } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; // test(300); ll x, y, k, p; cin >> x >> y >> k >> p; if(y%2 == -1) p *= -1; if(solve0(x, y, k, p)) cout << "Alice" << endl; else cout << "Bob" << endl; }