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.)

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分