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 0

-----Sample Output----- 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.