#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion #include #include namespace set_function { template void subset_zeta_transform(std::vector& f) { int n = f.size(); assert((n & (n - 1)) == 0); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { f[j | i] += f[j]; } } } } template void subset_mobius_transform(std::vector& f) { int n = f.size(); assert((n & (n - 1)) == 0); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { f[j | i] -= f[j]; } } } } template void superset_zeta_transform(std::vector& f) { int n = f.size(); assert((n & (n - 1)) == 0); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { f[j] += f[j | i]; } } } } template void superset_mobius_transform(std::vector& f) { int n = f.size(); assert((n & (n - 1)) == 0); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { f[j] -= f[j | i]; } } } } template void walsh_hadamard_transform(std::vector& f, bool inv = false) { int n = f.size(); assert((n & (n - 1)) == 0); for (int i = 1; i < n; i <<= 1) { for (int j = 0; j < n; j++) { if ((j & i) == 0) { T x = f[j], y = f[j | i]; f[j] = x + y, f[j | i] = x - y; } } } if (inv) { if (std::is_integral::value) { for (auto& x : f) x /= n; } else { T inv_n = T(1) / f.size(); for (auto& x : f) x *= inv_n; } } } template std::vector and_convolution(std::vector f, std::vector g) { assert(f.size() == g.size()); superset_zeta_transform(f); superset_zeta_transform(g); for (size_t i = 0; i < f.size(); i++) f[i] *= g[i]; superset_mobius_transform(f); return f; } template std::vector or_convolution(std::vector f, std::vector g) { assert(f.size() == g.size()); subset_zeta_transform(f); subset_zeta_transform(g); for (size_t i = 0; i < f.size(); i++) f[i] *= g[i]; subset_mobius_transform(f); return f; } template std::vector xor_convolution(std::vector f, std::vector g) { assert(f.size() == g.size()); walsh_hadamard_transform(f); walsh_hadamard_transform(g); for (size_t i = 0; i < f.size(); i++) f[i] *= g[i]; walsh_hadamard_transform(f, true); return f; } } // namespace set_function /** * @brief set function (FZT, FMT, FWHT) * @docs docs/convolution/set_function.md */ const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; // const long long MOD = 1000000007; const long long MOD = 998244353; const int MAX_B = 18; int main() { cin.tie(0); ios::sync_with_stdio(false); int N, X; cin >> N >> X; vector A(N); for (int i = 0; i < N; i++) cin >> A[i]; long long ans = 0; vector cnt(1 << MAX_B, 0); for (int i = 0; i < N; i++) cnt[A[i]]++; vector conv = set_function::xor_convolution(cnt, cnt); for (int i = 0; i < X; i++) ans += conv[i] * i; for (int j = 0, mask = 1; j < MAX_B; j++, mask <<= 1) { fill(cnt.begin(), cnt.end(), 0); for (int i = 0; i < N; i++) { if (A[i] & mask) { cnt[A[i]]++; ans -= mask; } } conv = set_function::xor_convolution(cnt, cnt); for (int i = 0; i < X; i++) ans += conv[i] * mask; } cout << ans / 2 << '\n'; return 0; }