Problem Description

You are given natural numbers $N$ and $X$, and a sequence $(a_1, a_2, \ldots, a_N)$ as input. Some of the $a_i$ are missing. It is known that the missing $a_i$ are in the range $0 \leq a_i \leq X$.

Restore the sequence so that it satisfies:

$a_1 \text{ XOR } a_2 \text{ XOR } \cdots \text{ XOR } a_N = X$

XOR is defined as the bitwise exclusive OR of integers $A$ and $B$. The result $X$ is defined as follows:

• In the binary representation of $X$, the digit at the $2^k$ (for $k \geq 0$) position is 1 if only one of the digits at the $2^k$ position in the binary representations of $A$ and $B$ is 1; otherwise, it is 0.

For example, $3 \text{ XOR } 5 = 6$ (in binary: $011 \text{ XOR } 101 = 110$).

Input Format

The input is given from the standard input in the following format:

$N$ $X$ $a_1$ $a_2$ $\ldots$ $a_N$

Output Format

Output one sequence that satisfies the condition. If no such sequence exists, output -1.

Sample Input and Output

Sample Input #1

4 11
8 -1 1 5

Sample Output #1

8 7 1 5

Sample Input #2

6 7
-1 2 -1 4 -1 6

Sample Output #2

1 2 3 4 5 6

Sample Input #3

1 2
3

Sample Output #3

-1

Notes/Hints

Constraints

• All input values are integers.
• $1 \leq N \leq 5 \times 10^5$
• $0 \leq X \leq 10^9$
• $-1 \leq a_i \leq 10^9$
  $a_i = -1$ means the information is missing.

见题面 Input 部分

见题面 Output 部分