#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include constexpr long long INF = 1LL << 60; double PI = acos(-1.0); #define rep(i, n) for (ll i = 0; i < (n); ++i) #define rep1(i, n) for (ll i = 1; i <= (n); ++i) #define rrep(i, n) for (ll i = (n - 1); i >= 0; --i) #define perm(c) sort(ALL(c));for(bool c##p=1;c##p;c##p=next_permutation(ALL(c))) #define ALL(obj) (obj).begin(), (obj).end() #define RALL(obj) (obj).rbegin(), (obj).rend() #define pb push_back #define to_s to_string #define len(v) (ll)v.size() #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define print(x) cout << (x) << '\n' #define drop(x) cout << (x) << '\n', exit(0) #define debug(x) cout << #x << ": " << (x) << '\n' using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair P; typedef tuple tpl; typedef vector vec; typedef vector> vec2; typedef vector>> vec3; template inline bool chmax(S &a, const T &b) { if (a inline bool chmin(S &a, const T &b) { if (b ostream &operator << (ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator >> (istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T1, typename T2, typename T3 > ostream &operator << (ostream &os, const tuple< T1, T2, T3 > &t) { os << get<0>(t) << " " << get<1>(t) << " " << get<2>(t); return os; } template< typename T1, typename T2, typename T3 > istream &operator >> (istream &is, tuple< T1, T2, T3 > &t) { is >> get<0>(t) >> get<1>(t) >> get<2>(t); return is; } template< typename T > ostream &operator << (ostream &os, const vector< T > &v){ for (int i = 0; i < (int)v.size(); ++i) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator >> (istream &is, vector< T > &v){ for(T &in : v) is >> in; return is; } template< typename T > ostream &operator << (ostream &os, const set< T > &st){ int ct = 0; for(auto& s : st) cout << s << (++ct != st.size() ? " " : ""); return os; } template constexpr set &operator|= (set &st1, const set &st2) { for(auto& s : st2) st1.insert(s); return st1; } template constexpr set &operator-= (set &st1, const set &st2) { for(auto& s : st2) if(st1.count(s)) st1.erase(s); return st1; } template constexpr set &operator&= (set &st1, const set &st2) { auto itr = st1.begin(); while(itr != st1.end()){ if(!st2.count(*itr)) itr = st1.erase(itr); else ++itr; } return st1; } template constexpr set operator| (const set &st1, const set &st2) { set res = st1; res |= st2; return res; } template constexpr set operator- (const set &st1, const set &st2) { set res = st1; res -= st2; return res; } template constexpr set operator& (const set &st1, const set &st2) { set res = st1; res &= st2; return res; } /*--------------------------------- Tools ------------------------------------------*/ template< typename T > vector cumsum(const vector &X){ vector res(X.size() + 1, 0); for(int i = 0; i < X.size(); ++i) res[i + 1] += res[i] + X[i]; return res; } template< typename S, typename T, typename F> pair bisearch(S left, T right, F f) { while(abs(right - left) > 1){ T mid = (right + left) / 2; if(f(mid)) right = mid; else left = mid; } return {left, right}; } template< typename S, typename T, typename F> double trisearch(S left, T right, F f, int maxLoop = 90){ double low = left, high = right; while(maxLoop--){ double mid_left = high / 3 + low * 2 / 3; double mid_right = high * 2 / 3 + low / 3; if(f(mid_left) >= f(mid_right)) low = mid_left; else high = mid_right; } return (low + high) * 0.5; } template< typename F > ll ternarySearch(ll L, ll R, F f) { //[L, R) ll lo = L - 1, hi = R - 1; while (lo + 1 != hi) { ll mi = (lo + hi) / 2; if (f(mi) <= f(mi + 1)) hi = mi; else lo = mi; } return hi; } // #include // using namespace atcoder; constexpr long long MOD = 1000000007; /*------------------------------- Main Code Here -----------------------------------------*/ int main() { ll N, X, Y; cin >> N >> X >> Y; vec A(N); cin >> A; // 後ろから見ていく // orを取ったら,1の桁は確定とみなせる // andを取ったら,0の桁は確定とみなせる // 確定していない桁がある場合,確定させるような操作しかできない // クエリ3については,その時点での結果 x A[i] = Yになるか調べていく. // 各bitについてorを確定したかどうかの状態を持たせる bool found = false; vec ret; auto dfs = [&](auto &&self, ll i, ll state, ll val)->void{ if(found) return; ll now = i == -1 ? X : A[i]; ll judge = val; rep(bit, 63){ if(!(state & (1LL << bit)) and (now & (1LL << bit))){ judge += 1LL << bit; } } if(judge == Y){ ret.pb(3); found = true; while(len(ret) < N) ret.pb(3); reverse(ALL(ret)); print(ret); return; } if(i == -1) return; ll sor = state; ll val_ = val; bool isor = false; rep(bit, 63) if (!(state & (1LL << bit))){ //orを使うとき,未確定かつ1の桁が増えるなら状態に加える if (A[i] & (1LL << bit)){ sor += 1LL << bit; val_ += 1LL << bit; isor = true; } } if(isor){ ret.pb(2); self(self, i - 1, sor, val_); ret.pop_back(); } ll sand = state; bool isand = false; rep(bit, 64) if (!(state & (1LL << bit))){ //andを使うとき,未確定かつ0の桁が増えるなら状態に加える if(!(A[i] & (1LL << bit))){ sand += 1LL << bit; isand = true; } } if(isand){ ret.pb(1); self(self, i - 1, sand, val); ret.pop_back(); } }; dfs(dfs, N - 1, 0, 0); if(!found) drop(-1); return 0; }