#include <bits/stdc++.h>
using namespace std;
const int nax = (1 << 19);
int a[nax];
int n, k;
struct node {
  node *lft, *rgt;
  int prefix, len;
  vector<int> mini, maxi, ans, numbers;
};
node* root;
void dfs(node* cur) {
  if (cur->len == k) {
    cur->mini.resize(1);
    cur->maxi.resize(1);
    cur->ans.resize(1);
    cur->mini[0] = 0;
    cur->maxi[0] = 0;
    cur->ans[0] = 1e9;
    return;
  }
  if (cur->len > k) return;
  if (cur->numbers.empty()) return;
  cur->rgt = new node;
  cur->lft = new node;
  for (int x : cur->numbers) {
    int v = (x & (1 << (k - cur->len - 1)));
    if (v) {
      cur->rgt->numbers.push_back(x ^ v);
    } else
      cur->lft->numbers.push_back(x ^ v);
  }
  cur->lft->len = cur->rgt->len = cur->len + 1;
  cur->lft->prefix = cur->prefix * 2;
  cur->rgt->prefix = cur->prefix * 2 + 1;
  dfs(cur->lft);
  dfs(cur->rgt);
  int sz = (1 << (k - cur->len));
  cur->mini.resize(sz, 1e9);
  cur->maxi.resize(sz, -1e9);
  cur->ans.resize(sz, 1e9);
  if (cur->lft->numbers.size()) {
    for (int i = 0; i < sz / 2; i++) {
      cur->ans[i] = min(cur->ans[i], cur->lft->ans[i]);
      cur->ans[i + sz / 2] = min(cur->ans[i + sz / 2], cur->lft->ans[i]);
    }
  }
  if (cur->rgt->numbers.size()) {
    for (int i = 0; i < sz / 2; i++) {
      cur->ans[i] = min(cur->ans[i], cur->rgt->ans[i]);
      cur->ans[i + sz / 2] = min(cur->ans[i + sz / 2], cur->rgt->ans[i]);
    }
  }
  int ful = (sz / 2 - 1);
  for (int i = 0; i < sz; i++) {
    int B = (i & (sz / 2));
    if (cur->lft->numbers.size()) {
      cur->mini[i] = min(cur->mini[i], B + cur->lft->mini[i & ful]);
      cur->maxi[i] = max(cur->maxi[i], B + cur->lft->maxi[i & ful]);
    }
    if (cur->rgt->numbers.size()) {
      cur->mini[i] = min(cur->mini[i], sz / 2 - B + cur->rgt->mini[i & ful]);
      cur->maxi[i] = max(cur->maxi[i], sz / 2 - B + cur->rgt->maxi[i & ful]);
    }
    if (cur->lft->numbers.size() && cur->rgt->numbers.size()) {
      if (B == 0)
        cur->ans[i] = min(cur->ans[i], cur->rgt->mini[i & ful] + sz / 2 -
                                           cur->lft->maxi[i & ful]);
      else
        cur->ans[i] = min(cur->ans[i], cur->lft->mini[i & ful] + sz / 2 -
                                           cur->rgt->maxi[i & ful]);
    }
  }
}
void solve() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  root = new node;
  root->prefix = 0;
  root->len = 0;
  root->numbers.resize(n);
  for (int i = 0; i < n; i++) root->numbers[i] = a[i];
  dfs(root);
  for (int i = 0; i < (1 << k); i++) cout << root->ans[i] << " ";
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int tt = 1;
  while (tt--) solve();
  return 0;
}
