101894: [AtCoder]ABC189 E - Rotate and Flip

Problem Statement

There are $N$ pieces on a two-dimensional plane. The coordinates of Piece $i$ are $(X_i,Y_i)$. There may be multiple pieces at the same coordinates.

We will do $M$ operations $\mathrm{op}_1, \ldots, \mathrm{op}_M$, one by one. There are four kinds of operations, described below along with their formats in input.

• 1：Rotate every piece $90$ degrees clockwise about the origin;
• 2：Rotate every piece $90$ degrees counterclockwise about the origin;
• 3 p：Move each piece to the point symmetric to it about the line $x=p$;
• 4 p：Move each piece to the point symmetric to it about the line $y=p$.

You are given $Q$ queries. In the $i$-th query, given two integers $A_i$ and $B_i$, print the coordinates of Piece $B_i$ just after the $A_i$-th operation. Here, the moment just before the $1$-st operation is considered to be the moment just after "the $0$-th operation".

Constraints

• All values in input are integers.
• $1 \leq N \leq 2\times 10^5$
• $1 \leq M \leq 2\times 10^5$
• $1 \leq Q \leq 2\times 10^5$
• $-10^9 \leq X_i,Y_i \leq 10^9$
• $\mathrm{op}_i$ is in the format of one of the four kinds of operations.
• In an operation with the form 3 p or 4 p, $-10^9 \leq p \leq 10^9$.
• $0 \leq A_i \leq M$
• $1 \leq B_i \leq N$

Input

Input is given from Standard Input in the following format:

$N$
$X_1$ $Y_1$
$\vdots$
$X_N$ $Y_N$
$M$
$\mathrm{op}_1$
$\vdots$
$\mathrm{op}_M$
$Q$
$A_1$ $B_1$
$\vdots$
$A_Q$ $B_Q$

Output

Print the response to each query in its own line: the $x$- and $y$-coordinates, in this order, with space in between.

Sample Input 1

1
1 2
4
1
3 3
2
4 2
5
0 1
1 1
2 1
3 1
4 1

Sample Output 1

1 2
2 -1
4 -1
1 4
1 0

Initially, the only piece - Piece $1$ - is at $(1, 2)$. Each operation moves the piece as follows: $(1,2)\to(2,-1)\to(4,-1)\to(1,4)\to(1,0)$.

Sample Input 2

2
1000000000 0
0 1000000000
4
3 -1000000000
4 -1000000000
3 1000000000
4 1000000000
2
4 1
4 2

Sample Output 2

5000000000 4000000000
4000000000 5000000000