A12593. Ehab and the Expected XOR Problem

Given two integers $n$ and $x$ , construct an array that satisfies the following conditions:

- for any element $a_i$ in the array, $1 \le a_i<2^n$ ;
- there is no non-empty subsegment with [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) equal to $0$ or $x$ ,
- its length $l$ should be maximized.

A sequence $b$ is a subsegment of a sequence $a$ if $b$ can be obtained from $a$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

The only line contains two integers $n$ and $x$ ( $1 \le n \le 18$ , $1 \le x<2^{18}$ ).

The first line should contain the length of the array $l$ .

If $l$ is positive, the second line should contain $l$ space-separated integers $a_1$ , $a_2$ , $\dots$ , $a_l$ ( $1 \le a_i < 2^n$ ) — the elements of the array $a$ .

If there are multiple solutions, print any of them.

In the first example, the bitwise XOR of the subsegments are $\{6,7,4,1,2,3\}$ .