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

3 10
3 3
2 5
1 12

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

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

Sample Output 2

0
2
1
0
5
3
3
11
2