description: You are given an array a consisting of n distinct elements and an integer k. Each element in the array is a non-negative integer not exceeding 2^k-1.
  
  Let's define the XOR distance for a number x as the value of 
  
  $$$f(x) = min_{i = 1}^{n} min_{j = i + 1}^{n} |(a_i ⊕ x) - (a_j ⊕ x)|,$$$
  
  where ⊕ denotes [the bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
  
  For every integer x from 0 to 2^k-1, you have to calculate f(x).
  
  Input
  
  The first line contains two integers n and k (1 ≤ k ≤ 19; 2 ≤ n ≤ 2^k).
  
  The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 2^k-1). All these integers are distinct.
  
  Output
  
  Print 2^k integers. The i-th of them should be equal to f(i-1).
  
  Examples
  
  Input
  
  
  3 3
  6 0 3
  
  
  Output
  
  
  3 1 1 2 2 1 1 3 
  
  
  Input
  
  
  3 4
  13 4 2
  
  
  Output
  
  
  2 2 6 6 3 1 2 2 2 2 1 3 6 6 2 2 
  
  Note
  
  Consider the first example:
  
    * for x = 0, if we apply bitwise XOR to the elements of the array with x, we get the array [6, 0, 3], and the minimum absolute difference of two elements is 3; 
    * for x = 1, if we apply bitwise XOR to the elements of the array with x, we get the array [7, 1, 2], and the minimum absolute difference of two elements is 1; 
    * for x = 2, if we apply bitwise XOR to the elements of the array with x, we get the array [4, 2, 1], and the minimum absolute difference of two elements is 1; 
    * for x = 3, if we apply bitwise XOR to the elements of the array with x, we get the array [5, 3, 0], and the minimum absolute difference of two elements is 2; 
    * for x = 4, if we apply bitwise XOR to the elements of the array with x, we get the array [2, 4, 7], and the minimum absolute difference of two elements is 2; 
    * for x = 5, if we apply bitwise XOR to the elements of the array with x, we get the array [3, 5, 6], and the minimum absolute difference of two elements is 1; 
    * for x = 6, if we apply bitwise XOR to the elements of the array with x, we get the array [0, 6, 5], and the minimum absolute difference of two elements is 1; 
    * for x = 7, if we apply bitwise XOR to the elements of the array with x, we get the array [1, 7, 4], and the minimum absolute difference of two elements is 3. 
solution: /**
   * author: derrick20
   * created: 8/3/21 10:08 PM
   */
  import java.io.*;
  import java.util.*;
  import static java.lang.Math.*;
  
  public class H_XORDistance {
      static FastScanner sc = new FastScanner();
      static PrintWriter out = new PrintWriter(System.out);
      
      public static void main(String[] args) {
          int elems = sc.nextInt();
          int n = sc.nextInt();
          int N = 1 << n;
          // explicit version first: subtree level, mask
          int[][] extrema = new int[N][2];
          int[] dp = new int[N];
          int oo = (int) 1e6;
          Arrays.setAll(extrema, i -> new int[]{oo, -oo});
          Arrays.fill(dp, oo);
          for (int i = 0; i < elems; i++) {
              int x = sc.nextInt();
              extrema[x] = new int[]{0, 0};
          }
          for (int k = 1; k <= n; k++) {
              int b = 1 << (k - 1);
              for (int x = 0; x < N; x++) {
                  if ((x & b) == 0) {
                      int y = x ^ b;
                      int interPairs = min(dp[x], dp[y]);
                      dp[y] = min(interPairs, (extrema[x][0] ^ b) - extrema[y][1]);
                      dp[x] = min(interPairs, (extrema[y][0] ^ b) - extrema[x][1]);
                      // oops not very nice
                      int[] ys = {extrema[y][0], extrema[y][1]};
                      int[] xs = {extrema[x][0], extrema[x][1]};
                      extrema[x] = new int[]{min(extrema[x][0], ys[0] ^ b), max(extrema[x][1], ys[1] ^ b)};
                      extrema[y] = new int[]{min(extrema[y][0], xs[0] ^ b), max(extrema[y][1], xs[1] ^ b)};
                  }
              }
  //            System.out.println(Arrays.toString(dp[k]));
          }
          for (int x = 0; x < N; x++) {
              out.print(dp[x] + " ");
          }
          out.println();
          out.close();
      }
  
      static class FastScanner {
          private int BS = 1 << 16;
          private char NC = (char) 0;
          private byte[] buf = new byte[BS];
          private int bId = 0, size = 0;
          private char c = NC;
          private double cnt = 1;
          private BufferedInputStream in;
      
          public FastScanner() {
              in = new BufferedInputStream(System.in, BS);
          }
      
          public FastScanner(String s) {
              try {
                  in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
              } catch (Exception e) {
                  in = new BufferedInputStream(System.in, BS);
              }
          }
      
          char getChar() {
              while (bId == size) {
                  try {
                      size = in.read(buf);
                  } catch (Exception e) {
                      return NC;
                  }
                  if (size == -1) return NC;
                  bId = 0;
              }
              return (char) buf[bId++];
          }
      
          int nextInt() {
              return (int) nextLong();
          }
      
          long nextLong() {
              cnt = 1;
              boolean neg = false;
              if (c == NC) c = getChar();
              for (; (c < '0' || c > '9'); c = getChar()) {
                  if (c == '-') neg = true;
              }
              long res = 0;
              for (; c >= '0' && c <= '9'; c = getChar()) {
                  res = (res << 3) + (res << 1) + c - '0';
                  cnt *= 10;
              }
              return neg ? -res : res;
          }
      
          double nextDouble() {
              boolean neg = false;
              if (c == NC) c = getChar();
              for (; (c < '0' || c > '9'); c = getChar()) {
                  if (c == '-') neg = true;
              }
              double cur = nextLong();
              if (c != '.') {
                  return neg ? -cur : cur;
              } else {
                  double frac = nextLong() / cnt;
                  return neg ? -cur - frac : cur + frac;
              }
          }
      
          String next() {
              StringBuilder res = new StringBuilder();
              while (c <= 32) c = getChar();
              while (c > 32) {
                  res.append(c);
                  c = getChar();
              }
              return res.toString();
          }
      
          String nextLine() {
              StringBuilder res = new StringBuilder();
              while (c <= 32) c = getChar();
              while (c != '\n') {
                  res.append(c);
                  c = getChar();
              }
              return res.toString();
          }
      
          boolean hasNext() {
              if (c > 32) return true;
              while (true) {
                  c = getChar();
                  if (c == NC) return false;
                  else if (c > 32) return true;
              }
          }
      }
      
      static void ASSERT(boolean assertion, String message) {
          if (!assertion) throw new AssertionError(message);
      }
      
      static void ASSERT(boolean assertion) {
          if (!assertion) throw new AssertionError();
      }
  }