#P1174D. Ehab and the Expected XOR Problem
Ehab and the Expected XOR Problem
Description
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 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.
Input
The only line contains two integers $n$ and $x$ ($1 \le n \le 18$, $1 \le x<2^{18}$).
Output
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.
Samples
3 5
3
6 1 3
2 4
3
1 3 1
1 1
0
Note
In the first example, the bitwise XOR of the subsegments are $\{6,7,4,1,2,3\}$.