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 $X$.

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.

3 10
3 3
2 5
1 12

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 $12$.

9 12
1 1
2 2
3 3
1 4
2 5
3 6
1 7
2 8
3 9

0
2
1
0
5
3
3
11
2