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

• for any element $a_i$ in the array, $1 \le a_i \lt 2^n$;
• 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 $x$ ($1 \le n \le 18$, $1 \le x \lt 2^{18}$).

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 $a_1$, $a_2$, $\dots$, $a_l$ ($1 \le a_i \lt 2^n$) — the elements of the array $a$.

If there are multiple solutions, print any of them.

Note

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