#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004004004004004LL; double EPS = 1e-16; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } // 手元環境(Visual Studio) #ifdef _MSC_VER #include "local.hpp" // 提出用(gcc) #else inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif #endif // 折りたたみ用 //--------------AtCoder 専用-------------- #include using namespace atcoder; //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } using vm = vector; using vvm = vector; using vvvm = vector; //---------------------------------------- void WA() { int n, x; cin >> n >> x; vi a(n); cin >> a; uniq(a); if (sz(a) < n) EXIT("No"); rep(i, n) dump(bitset<30>(a[i])); dump("-----"); dump(bitset<30>(x)); int m = msb(x); unordered_map ul; rep(i, n) { int u = a[i] >> m; if (ul.count(u)) { if (((a[i] >> (m - 1)) & 1) != ul[u]) EXIT("No"); } else { ul[u] = (a[i] >> (m - 1)) & 1; } } EXIT("Yes"); } void WA2() { int n, x; cin >> n >> x; vi a(n); cin >> a; try { sort(all(a), [&](auto const& l, auto const& r) { return l < (r^ x) && (l^ x) < r; }); } catch (...) { EXIT("No"); } rep(i, n) dump(bitset<30>(a[i])); dump("-----"); dump(bitset<30>(x)); // これでダメならダメやろたぶん. rep(i, n - 1) { int l = a[i], r = a[i + 1]; if (l < (r ^ x) && (l ^ x) < r) continue; EXIT("No"); } EXIT("Yes"); } void WA3() { int n, x; cin >> n >> x; vi a(n); cin >> a; uniq(a); if (sz(a) < n) EXIT("No"); rep(i, n) dump(bitset<30>(a[i])); dump("-----"); dump(bitset<30>(x)); int m = msb(x); unordered_map ul; rep(i, n) ul[a[i] >> m].push_back(a[i] & ((1 << m) - 1)); dumpel(ul); // より下位のビットも考慮しなきゃだめそうだけど,試しに提出. repe(tmp, ul) { vi cnt(2); repe(x, tmp.second) cnt[(x >> (m - 1)) & 1]++; if (abs(cnt[1] - cnt[0]) > 1) EXIT("No"); } EXIT("Yes"); } int main() { // input_from_file("input.txt"); // output_to_file("output.txt"); int n, x; cin >> n >> x; vi a(n); cin >> a; function rf = [&](int l, int r, int mask, int b) { if (b == -1) return; if (x & (1 << b)) { mask += 1 << b; rf(l, r, mask, b - 1); return; } sort(a.begin() + l, a.begin() + r, [&](auto const& a1, auto const& a2) { return (a1 & (1 << b)) < (a2 & (1 << b)); }); auto it = lower_bound(a.begin() + l, a.begin() + r, 1 << b, [&](auto const& a1, auto const& a2) { return (a1 & (1 << b)) < (a2 & (1 << b)); }); int m = (int)distance(a.begin(), it); if (l < m) { if (mask != 0 || b == 0) { unordered_map cnt_lm(2); repi(i, l, m - 1) cnt_lm[a[i] & mask]++; if (sz(cnt_lm) > 2) EXIT("No"); if (sz(cnt_lm) == 2) { vi vs, cs; repe(tmp, cnt_lm) { vs.push_back(tmp.first); cs.push_back(tmp.second); } if ((vs[0] ^ vs[1]) != mask) EXIT("No"); if (abs(cs[0] - cs[1]) > 1) EXIT("No"); } if (sz(cnt_lm) == 1 && cnt_lm.begin()->second > 1) EXIT("No"); } rf(l, m, mask, b - 1); } if (m < r) { if (mask != 0 || b == 0) { unordered_map cnt_mr(2); repi(i, m, r - 1) cnt_mr[a[i] & mask]++; if (sz(cnt_mr) > 2) EXIT("No"); if (sz(cnt_mr) == 2) { vi vs, cs; repe(tmp, cnt_mr) { vs.push_back(tmp.first); cs.push_back(tmp.second); } if ((vs[0] ^ vs[1]) != mask) EXIT("No"); if (abs(cs[0] - cs[1]) > 1) EXIT("No"); } if (sz(cnt_mr) == 1 && cnt_mr.begin()->second > 1) EXIT("No"); } rf(m, r, mask, b - 1); } }; rf(0, n, 0, 29); Yes(1); }