#include <bits/stdc++.h>
#pragma GCC optimize(2)
using namespace std;
const int maxn = (1 << 19) + 5;
int ch[maxn << 1][2], maxi[maxn << 1], mini[maxn << 1], ans[maxn << 1];
int k;
int out[maxn], cnt;
void update(int x, int l, int r) {
  int mid = (l + r) >> 1;
  maxi[x] = max(maxi[ch[x][0]], maxi[ch[x][1]] + (mid - l + 1));
  mini[x] = min(mini[ch[x][0]], mini[ch[x][1]] + (mid - l + 1));
  ans[x] = min(ans[ch[x][0]], ans[ch[x][1]]);
  ans[x] = min(ans[x], mini[ch[x][1]] + (mid - l + 1) - maxi[ch[x][0]]);
}
void update(int &x, int l, int r, int iter) {
  if (!x) x = ++cnt;
  if (l == r) {
    maxi[x] = mini[x] = 0;
    ans[x] = 1e9;
    return;
  }
  int mid = (l + r) >> 1;
  if (mid >= iter)
    update(ch[x][0], l, mid, iter);
  else
    update(ch[x][1], mid + 1, r, iter);
  update(x, l, r);
}
void swap(int x, int l, int r, int to) {
  if (!x) return;
  int mid = (l + r) >> 1;
  if ((r - l + 1) == (1 << to))
    swap(ch[x][0], ch[x][1]);
  else {
    swap(ch[x][0], l, mid, to);
    swap(ch[x][1], mid + 1, r, to);
  }
  update(x, l, r);
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n >> k;
  mini[0] = 1e9;
  maxi[0] = -1e9;
  ans[0] = 1e9;
  int root = 0, m = (1 << k) - 1;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    update(root, 0, m, x);
  }
  cout << ans[root] << ' ';
  int lst = 0;
  for (int x = 1; x <= m; x++) {
    int to = 0;
    for (int j = 0; j < k; j++)
      if (x & (1 << j)) to ^= 1 << (k - j - 1);
    for (int j = 0; j < k; j++)
      if ((lst & (1 << j)) != (to & (1 << j))) {
        swap(root, 0, m, j + 1);
      }
    out[to] = ans[root];
    lst = to;
  }
  for (int i = 1; i <= m; i++) cout << out[i] << ' ';
  return 0;
}
