Problem Statement

Construct a sequence $a$ = {$a_1,\\ a_2,\\ ...,\\ a_{2^{M + 1}}$} of length $2^{M + 1}$ that satisfies the following conditions, if such a sequence exists.

• Each integer between $0$ and $2^M - 1$ (inclusive) occurs twice in $a$.
• For any $i$ and $j$ $(i < j)$ such that $a_i = a_j$, the formula $a_i \\ xor \\ a_{i + 1} \\ xor \\ ... \\ xor \\ a_j = K$ holds.

What is xor (bitwise exclusive or)?

The xor of integers $c_1, c_2, ..., c_n$ is defined as follows:

• When $c_1 \\ xor \\ c_2 \\ xor \\ ... \\ xor \\ c_n$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if the number of integers among $c_1, c_2, ...c_m$ whose binary representations have $1$ in the $2^k$'s place is odd, and $0$ if that count is even.

For example, $3 \\ xor \\ 5 = 6$. (If we write it in base two: 011 $xor$ 101 \= 110.)

Constraints

• All values in input are integers.
• $0 \\leq M \\leq 17$
• $0 \\leq K \\leq 10^9$

Input

Input is given from Standard Input in the following format:

$M$ $K$

Output

If there is no sequence $a$ that satisfies the condition, print -1.

If there exists such a sequence $a$, print the elements of one such sequence $a$ with spaces in between.

If there are multiple sequences that satisfies the condition, any of them will be accepted.

Sample Input 1

1 0

Sample Output 1

0 0 1 1

For this case, there are multiple sequences that satisfy the condition.

For example, when $a$ = {$0, 0, 1, 1$}, there are two pairs $(i,\\ j)\\ (i < j)$ such that $a_i = a_j$: $(1, 2)$ and $(3, 4)$. Since $a_1 \\ xor \\ a_2 = 0$ and $a_3 \\ xor \\ a_4 = 0$, this sequence $a$ satisfies the condition.

Sample Input 2

1 1

Sample Output 2

-1

No sequence satisfies the condition.

Sample Input 3

5 58

Sample Output 3

-1

No sequence satisfies the condition.