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Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

We have a variable $X$ and $N$ kinds of operations that change the value of $X$. Operation $i$ is represented as a pair of integers $(T_i,A_i)$, and is the following operation:

if $T_i=1$, it replaces the value of $X$ with $X\ {\rm and}\ A_i$;
if $T_i=2$, it replaces the value of $X$ with $X\ {\rm or}\ A_i$;
if $T_i=3$, it replaces the value of $X$ with $X\ {\rm xor}\ A_i$.

Initialize $X$ with the value of $C$ and execute the following procedures in order:

Perform Operation $1$, and then print the resulting value of $X$.
Next, perform Operation $1, 2$ in this order, and then print the value of $X$.
Next, perform Operation $1, 2, 3$ in this order, and then print the value of $X$.
$\vdots$
Next, perform Operation $1, 2, \ldots, N$ in this order, and then print the value of $X$.

What are ${\rm and}, {\rm or}, {\rm xor}$?

The ${\rm and}, {\rm or}, {\rm xor}$ of non-negative integers $A$ and $B$ are defined as follows:

When $A\ {\rm and}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if both of the digits in that place of $A$ and $B$ are $1$, and $0$ otherwise.
When $A\ {\rm or}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if at least one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise.
When $A\ {\rm xor}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise.

For example, $3\ {\rm and}\ 5 = 1$, $3\ {\rm or}\ 5 = 7$, and $3\ {\rm xor}\ 5 = 6$.

Constraints

$1 \leq N \leq 2\times 10^5$
$1\leq T_i \leq 3$
$0\leq A_i \lt 2^{30}$
$0\leq C \lt 2^{30}$
All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $C$
$T_1$ $A_1$
$T_2$ $A_2$
$\vdots$
$T_N$ $A_N$

Output

Print $N$ lines, as specified in the Problem Statement.

Sample Input 1

Sample Output 1

9
15
12

The initial value of $X$ is $10$.

Operation $1$ changes $X$ to $9$.
Next, Operation $1$ changes $X$ to $10$, and then Operation $2$ changes it to $15$.
Next, Operation $1$ changes $X$ to $12$, and then Operation $2$ changes it to $13$, and then Operation $3$ changes it to $12$.

Sample Input 2

Sample Output 2