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D - LRUD Instructions

Score : $400$ points

Problem Statement

There is a grid with $H$ horizontal rows and $W$ vertical columns. $(i, j)$ denotes the square at the $i$-th row from the top and $j$-th column from the left.
$N$ squares, $(r_1, c_1), (r_2, c_2), \ldots, (r_N, c_N)$, have walls.

Takahashi is initially at square $(r_\mathrm{s}, c_\mathrm{s})$.

$Q$ instructions are given to Takahashi. For $i = 1, 2, \ldots, Q$, the $i$-th instruction is represented by a pair of a character $d_i$ and a positive integer $l_i$. $d_i$ is one of L, R, U, and D, representing the directions of left, right, up, and down, respectively.

Given the $i$-th direction, Takahashi repeats the following action $l_i$ times:

If a square without a wall is adjacent to the current square in the direction represented by $d_i$, move to that square; otherwise, do nothing.

For $i = 1, 2, \ldots, Q$, print the square where Takahashi will be after he follows the first $i$ instructions.

Constraints

• $2 \leq H, W \leq 10^9$
• $1 \leq r_\mathrm{s} \leq H$
• $1 \leq c_\mathrm{s} \leq W$
• $0 \leq N \leq 2 \times 10^5$
• $1 \leq r_i \leq H$
• $1 \leq c_i \leq W$
• $i \neq j \Rightarrow (r_i, c_i) \neq (r_j, c_j)$
• $(r_\mathrm{s}, c_\mathrm{s}) \neq (r_i, c_i)$ for all $i = 1, 2, \ldots, N$.
• $1 \leq Q \leq 2 \times 10^5$
• $d_i$ is one of the characters L, R, U, and D.
• $1 \leq l_i \leq 10^9$
• All values in the input other than $d_i$ are integers.

---

Input

The input is given from Standard Input in the following format:

$H$ $W$ $r_\mathrm{s}$ $c_\mathrm{s}$

$N$

$r_1$ $c_1$

$r_2$ $c_2$

$\vdots$

$r_N$ $c_N$

$Q$

$d_1$ $l_1$

$d_2$ $l_2$

$\vdots$

$d_Q$ $l_Q$

Output

Print $Q$ lines. For $i = 1, 2, \ldots, Q$, the $i$-th line should contain the square $(R_i, C_i)$ where Takahashi will be after he follows the first $i$ instructions, in the following format:

``` $R_1$ $C_1$ $R_2$ $C_2$ $\vdots$ $R_Q$ $C_Q$ ```

---

5 5 4 4
3
5 3
2 2
1 4
4
L 2
U 3
L 2
R 4

4 2
3 2
3 1
3 5

The given grid and the initial position of Takahashi are as follows, where # denotes a square with a wall, T a square where Takahashi is, and . the other squares:

``` ...#. .#... ..... ...T. ..#.. ```

Given the $1$-st instruction, Takahashi moves $2$ squares to the left, ending up in square $(4, 2)$ as follows:

``` ...#. .#... ..... .T... ..#.. ```

Given the $2$-nd instruction, Takahashi first moves $1$ square upward, then he "does nothing" twice because the adjacent square in his direction has a wall. As a result, he ends up in square $(3, 2)$ as follows:

``` ...#. .#... .T... ..... ..#.. ```

Given the $3$-rd instruction, Takahashi first moves $1$ square to the left, then he "does nothing" once because there is no square in his direction. As a result, he ends up in square $(3, 1)$ as follows:

``` ...#. .#... T.... ..... ..#.. ```

Given the $4$-th instruction, Takahashi moves $4$ squares to the right, ending up in square $(3, 5)$ as follows:

``` ...#. .#... ....T ..... ..#.. ```

---

6 6 6 3
7
3 1
4 3
2 6
3 4
5 5
1 1
3 2
10
D 3
U 3
L 2
D 2
U 3
D 3
U 3
R 3
L 3
D 1

6 3
5 3
5 1
6 1
4 1
6 1
4 1
4 2
4 1
5 1