H. XOR and Distancetime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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\limits_{i = 1}^{n} \min\limits_{j = i + 1}^{n} |(a_i \oplus x) - (a_j \oplus x)|,where \oplus denotes the bitwise XOR operation.For every integer x from 0 to 2^k-1, you have to calculate f(x).InputThe first line contains two integers n and k (1 \le k \le 19; 2 \le n \le 2^k).The second line contains n integers a_1, a_2, \dots, a_n (0 \le a_i \le 2^k-1). All these integers are distinct.OutputPrint 2^k integers. The i-th of them should be equal to f(i-1).ExamplesInput
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 
NoteConsider 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. 
3 3
6 0 3

3 1 1 2 2 1 1 3  
['bitmasks', 'divide and conquer', 'trees', '*2900']