#include <bits/stdc++.h>
using namespace std;
int k;
struct node {
  node* c[2];
};
node* trie;
void ins(int r) {
  node* f = trie;
  for (int j = k - 1; j >= 0; j--) {
    if (!f->c[1 & (r >> j)]) {
      f->c[1 & (r >> j)] = new node();
      f->c[1 & (r >> j)]->c[0] = f->c[1 & (r >> j)]->c[1] = nullptr;
    }
    f = f->c[1 & (r >> j)];
  }
}
vector<vector<int> > ans;
void solve(node* l, node* r, int st, int x, int d, int diff) {
  if (d == k) {
    ans[st][x] = min(ans[st][x], diff);
  } else {
    for (int j = 0; j < 2; j++) {
      if (l->c[1 ^ j] && r->c[0 ^ j]) {
        solve(l->c[1 ^ j], r->c[0 ^ j], st, x ^ (j << (k - 1 - d)), d + 1,
              diff - (1 << (k - 1 - d)));
        continue;
      }
      if (l->c[1 ^ j] && r->c[1 ^ j]) {
        solve(l->c[1 ^ j], r->c[1 ^ j], st, x ^ (j << (k - 1 - d)), d + 1,
              diff);
        continue;
      }
      if (l->c[0 ^ j] && r->c[0 ^ j]) {
        solve(l->c[0 ^ j], r->c[0 ^ j], st, x ^ (j << (k - 1 - d)), d + 1,
              diff);
        continue;
      }
      if (l->c[0 ^ j] && r->c[1 ^ j]) {
        solve(l->c[0 ^ j], r->c[1 ^ j], st, x ^ (j << (k - 1 - d)), d + 1,
              diff + (1 << (k - 1 - d)));
        continue;
      }
    }
  }
}
void tr(node* v, int r, int d) {
  if (v->c[0] && v->c[1]) {
    solve(v->c[0], v->c[1], d, 0, d + 1, (1 << (k - 1 - d)));
    solve(v->c[1], v->c[0], d, (1 << (k - 1 - d)), d + 1, (1 << (k - 1 - d)));
  }
  if (v->c[0]) tr(v->c[0], 2 * r + 0, d + 1);
  if (v->c[1]) tr(v->c[1], 2 * r + 1, d + 1);
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(nullptr);
  trie = new node();
  trie->c[0] = trie->c[1] = nullptr;
  int n;
  cin >> n >> k;
  ans.assign(k, vector<int>(1 << k, int(1e8)));
  vector<int> a(n);
  for (int& x : a) cin >> x;
  sort(a.begin(), a.end());
  for (int x : a) ins(x);
  assert(trie != nullptr);
  tr(trie, 0, 0);
  for (int i = 0; i < (1 << k); i++) {
    int best = int(1e8);
    for (int j = 0; j < k; j++) {
      best = min(best, ans[j][i % (1 << (k - j))]);
    }
    cout << best << ' ';
  }
  cout << '\n';
}
