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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分