#include using namespace std; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) (a).begin(), (a).end() #define Sort(a) (sort((a).begin(), (a).end())) #define RSort(a) (sort((a).rbegin(), (a).rend())) #define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end())) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T &a){ return *min_element(a.begin(), a.end()); } template auto max(const T &a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); 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; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; 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 map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template long long binary_search(long long ok, long long ng, T check){ while(abs(ok - ng) > 1){ long long mid = (ok + ng) / 2; if(check(mid)) ok = mid; else ng = mid; } return ok; } template long double binary_search_real(long double ok, long double ng, T check, int iter = 100){ for(int i = 0; i < iter; ++i){ long double mid = (ok + ng) / 2; if(check(mid)) ok = mid; else ng = mid; } return ok; } template long long trisum(T a, T b){ long long res = ((b - a + 1) * (a + b)) / 2; return res; } template T intpow(T x, int n){ T ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } template T getReminder(T a, T b){ if(b == 0) return -1; if(a >= 0 && b > 0){ return a % b; } else if(a < 0 && b > 0){ return ((a % b) + b) % b; } else if(a >= 0 && b < 0){ return a % b; } else{ return (abs(b) - abs(a % b)) % b; } } template inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector> &G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } // https://ei1333.github.io/library/structure/trie/binary-trie.hpp.html template struct BinaryTrie { public: struct Node { Node *nxt[2]; D exist; vector accept; Node() : nxt{nullptr, nullptr}, exist(0) {} }; Node *root; explicit BinaryTrie() : root(new Node()) {} explicit BinaryTrie(Node *root) : root(root) {} void add(const T &bit, int idx = -1, D delta = 1, T xor_val = 0) { root = add(root, bit, idx, MAX_LOG, delta, xor_val); } void erase(const T &bit, T xor_val = 0) { add(bit, -1, -1, xor_val); } Node *find(const T &bit, T xor_val = 0) { return find(root, bit, MAX_LOG, xor_val); } D count(const T &bit, T xor_val = 0) { auto node = find(bit, xor_val); return node ? node->exist : 0; } pair min_element(T xor_val = 0) { assert(root->exist > 0); return kth_element(0, xor_val); } pair max_element(T xor_val = 0) { assert(root->exist > 0); return kth_element(root->exist - 1, xor_val); } pair kth_element(D k, T xor_val = 0) { // 0-indexed assert(0 <= k && k < root->exist); return kth_element(root, k, MAX_LOG, xor_val); } D count_less(const T &bit, T xor_val = 0) { // < bit return count_less(root, bit, MAX_LOG, xor_val); } private: virtual Node *clone(Node *t) { return t; } Node *add(Node *t, T bit, int idx, int depth, D x, T xor_val, bool need = true) { if (need) t = clone(t); if (depth == -1) { t->exist += x; if (idx >= 0) t->accept.emplace_back(idx); } else { bool f = (xor_val >> depth) & 1; auto &to = t->nxt[f ^ ((bit >> depth) & 1)]; if (!to) to = new Node(), need = false; to = add(to, bit, idx, depth - 1, x, xor_val, need); t->exist += x; } return t; } Node *find(Node *t, T bit, int depth, T xor_val) { if (depth == -1) { return t; } else { bool f = (xor_val >> depth) & 1; auto &to = t->nxt[f ^ ((bit >> depth) & 1)]; return to ? find(to, bit, depth - 1, xor_val) : nullptr; } } pair kth_element(Node *t, D k, int bit_index, T xor_val) { // 0-indexed if (bit_index == -1) { return {0, t}; } else { bool f = (xor_val >> bit_index) & 1; if ((t->nxt[f] ? t->nxt[f]->exist : 0) <= k) { auto ret = kth_element(t->nxt[f ^ 1], k - (t->nxt[f] ? t->nxt[f]->exist : 0), bit_index - 1, xor_val); ret.first |= T(1) << bit_index; return ret; } else { return kth_element(t->nxt[f], k, bit_index - 1, xor_val); } } } D count_less(Node *t, const T &bit, int bit_index, T xor_val) { if (bit_index == -1) return 0; D ret = 0; bool f = (xor_val >> bit_index) & 1; if ((bit >> bit_index & 1) and t->nxt[f]) ret += t->nxt[f]->exist; if (t->nxt[f ^ (bit >> bit_index & 1)]) ret += count_less(t->nxt[f ^ (bit >> bit_index & 1)], bit, bit_index - 1, xor_val); return ret; } }; ll T; void input(){ in(T); } void solve(){ ll n, k; in(n, k); vll a(n); in(a); Sort(a); BinaryTrie bt; rep(i, n) bt.add(a[i]); auto f = [&](ll x){ ll s = 0; rep(i, n){ if(s + (n * (n - i)) < k){ return false; } s += bt.count_less(x + 1, a[i]); if(s >= (k * 2) + n){ return true; } } return false; }; out(binary_search(1LL << 30, -1LL, f)); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); T = 1; // input(); while(T--) solve(); }