D. Ehab and the Expected XOR Problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
3 5
Output
3
6 1 3
Input
2 4
Output
3
1 3 1
Input
1 1
Output
0
Note

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