#include <bits/stdc++.h>
using namespace std;
template <typename T>
using minPq = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
inline void UNIQUE(vector<T> &v) {
  sort((v).begin(), (v).end());
  v.resize(unique((v).begin(), (v).end()) - v.begin());
}
inline constexpr int lg2(int x) { return 32 - __builtin_clz(x); }
inline constexpr long long lg2(long long x) { return 32 - __builtin_clzll(x); }
const int INF = 0x3f3f3f3f;
const long long LLINF = 0x3f3f3f3f3f3f3f3f;
const double PI = acos(-1);
int n, k;
struct Node {
  int dif, mn, mx;
};
bool input[1 << 19];
vector<Node> build(int l, int r) {
  int len = r - l;
  if (l + 1 == r) {
    vector<Node> res;
    if (input[l])
      res.push_back({INF, l, l});
    else
      res.push_back({INF, INF, INF});
    return res;
  }
  int mid = (l + r) / 2;
  vector<Node> lRes = build(l, mid);
  vector<Node> rRes = build(mid, r);
  vector<Node> ans;
  for (int i = 0; i < len / 2; ++i) {
    if (lRes[i].mn == INF && rRes[i].mn == INF)
      ans.push_back({INF, INF, INF});
    else if (lRes[i].mn == INF)
      ans.push_back(rRes[i]);
    else if (rRes[i].mn == INF)
      ans.push_back(lRes[i]);
    else {
      ans.push_back(
          {min(rRes[i].mn - lRes[i].mx, min(lRes[i].dif, rRes[i].dif)),
           lRes[i].mn, rRes[i].mx});
    }
  }
  for (int i = 0; i < len / 2; ++i) {
    if (lRes[i].mn == INF && rRes[i].mn == INF)
      ans.push_back({INF, INF, INF});
    else if (lRes[i].mn == INF)
      ans.push_back(
          {rRes[i].dif, rRes[i].mn ^ (len / 2), rRes[i].mx ^ (len / 2)});
    else if (rRes[i].mn == INF)
      ans.push_back(
          {lRes[i].dif, lRes[i].mn ^ (len / 2), lRes[i].mx ^ (len / 2)});
    else {
      ans.push_back({min((lRes[i].mn ^ (len / 2)) - (rRes[i].mx ^ (len / 2)),
                         min(lRes[i].dif, rRes[i].dif)),
                     rRes[i].mn ^ (len / 2), lRes[i].mx ^ (len / 2)});
    }
  }
  return ans;
}
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    input[a] = true;
  }
  auto ans = build(0, 1 << k);
  for (int i = 0; i < (1 << k); ++i) {
    cout << ans[i].dif << " \n"[i == (1 << k) - 1];
  }
}
