#include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for (int i = (begin), i##_end_ = (end); i < i##_end_; i++) #define IFOR(i, begin, end) for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--) #define REP(i, n) FOR(i, 0, n) #define IREP(i, n) IFOR(i, 0, n) #define ALL(x) (x).begin(), (x).end() // template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T& m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T& m, const T q) { return m > q ? (m = q, true) : false; } template pair operator+(const pair& l, const pair& r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair& l, const pair& r) { return make_pair(l.first - r.first, l.second - r.second); } template vector srtunq(vector vec) { return sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()), vec; } template istream& operator>>(istream& is, vector& vec) { return for_each(begin(vec), end(vec), [&](T& v) { is >> v; }), is; } // output template ostream& dmpseq(ostream&, const T&, const string&, const string&, const string&); #if __cplusplus >= 201703L template ostream& operator<<(ostream& os, const tuple& tpl) { return apply([&os](auto&&... args) { ((os << args << ','), ...); }, tpl), os; } #endif // template ostream& operator<<(ostream& os, const pair& p) { return os << '(' << p.first << ',' << p.second << ')'; } template ostream& operator<<(ostream& os, const vector& x) { return dmpseq, T>(os, x, "[", ",", "]"); } template ostream& operator<<(ostream& os, const deque& x) { return dmpseq, T>(os, x, "deq[", ",", "]"); } template ostream& operator<<(ostream& os, const set& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const unordered_set& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const multiset& x) { return dmpseq, T>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const map& x) { return dmpseq, pair>(os, x, "{", ",", "}"); } template ostream& operator<<(ostream& os, const unordered_map& x) { return dmpseq, pair>(os, x, "{", ",", "}"); } template ostream& dmpseq(ostream& os, const T& seq, const string& pre, const string& sp, const string& suf) { return os << pre, for_each(begin(seq), end(seq), [&](V x) { os << x << sp; }), os << suf; } template void print(const vector& x) { dmpseq, T>(cout, x, "", " ", "\n"); } #ifdef HITONANODE_LOCAL constexpr int D = 9; #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl #else constexpr int D = 19; #define dbg(x) {} #endif template void walsh_hadamard(std::vector& seq, F f) { const int n = seq.size(); assert(__builtin_popcount(n) == 1); for (int w = 1; w < n; w *= 2) { for (int i = 0; i < n; i += w * 2) { for (int j = 0; j < w; j++) { f(seq[i + j], seq[i + j + w]); } } } } // xor convolution // ret[i] = \sum_j x[j] * y[i ^ j] // if T is integer, ||x||_1 * ||y||_1 < numeric_limits::max() template std::vector xorconv(std::vector x, std::vector y) { const int n = x.size(); assert(__builtin_popcount(n) == 1); assert(x.size() == y.size()); auto f = [](T& lo, T& hi) { T c = lo + hi; hi = lo - hi, lo = c; }; if (x == y) { walsh_hadamard(x, f), y = x; } else { walsh_hadamard(x, f), walsh_hadamard(y, f); } for (size_t i = 0; i < x.size(); i++) { x[i] *= y[i]; } auto finv = [](T& lo, T& hi) { T c = lo + hi; hi = (lo - hi) / 2, lo = c / 2; }; walsh_hadamard(x, finv); return x; } int main() { int N, X; cin >> N >> X; vector A(N); cin >> A; vector cnt(1 << D); for (auto a : A) cnt[a]++; cnt = xorconv(cnt, cnt); cnt[0] -= N; lint ret = 0; REP(d, D) { vector cntd(1 << D); int nd = 0; for (auto a : A) if (((a >> d) & 1) == 0) { cntd[a]++, nd++; } cntd = xorconv(cntd, cntd); cntd[0] -= nd; REP(i, X) { ret += (1LL << d) * (cnt[i] - cntd[i]) / 2; } } cout << ret << '\n'; }