# 50085. Tank Simulation

## I'm a slow walker, but I never walk backwards.

Write a program to simulate a tank movement on a map.

We have an $N$ by $M$ map with an $L$ by $W$ tank and $O$ obstacles in it. The vertical index is from $0$ to $N - 1$, and the horizontal index is from $0$ to $M - 1$. An integer in every cell of the map indicates the status of the cell, where $0$ is an empty space, $1$ is tank, and $2$ is an obstacle. Note that we will use the upper left corner of the tank to indicate its position, and the initial position of the tank is $(0, 0)$. The tank will move according to instructions. Each instruction is a number from $0$ to $5$, indicating the direction the tank should go, or we should print the map. Let the current position of upper left corner of tank be $(x, y)$.

• If the instruction is $0$, output the current map information.
• If the instruction is $1$, the tank moves from $(x, y)$ to $(x + 1, y)$.
• If the instruction is $2$, the tank moves from $(x, y)$ to $(x, y + 1)$.
• If the instruction is $3$, the tank moves from $(x, y)$ to $(x - 1, y)$.
• If the instruction is $4$, the tank moves from $(x, y)$ to $(x, y - 1)$.
• If the instruction is $5$, the tank moves from $(x, y)$ to $(x + 1, y + 1)$.

The coordinate system is defined as follows:

p10172. Coordinate

Note that if an instruction moves the tank out of the map or hit more than one obstacles, the tank will not move. Otherwise the tank will move in the intended direction.

Write a program to simulate a tank movement on the map, and output the map information if instruction is $0$. The program simulates the tank, which is initially located at $(0, 0)$, and the movement according to the input instructions until the end of file. It is guaranteed that there is at least one instruction and the initial area of tank have no obstacles.

Take sample input 3 for example. The figure is shown below.

p10172. Tank

• 20 points: The tank size is $1$ by $1$ and only have instructions $0$~$4$.
• 50 points: The tank size is $L$ by $W$ and only have instructions $0$~$4$.
• 30 points: The tank size is $L$ by $W$ and have all instructions.

## Input Format

The input contains only one test case. The first line contains four integers $N$, $M$, $L$ and $W$ representing the length and width of map and tank. The second line contains one integer $O$ representing the number of obstacles. For the following $O$ lines, each line contains two integers, representing the $x$, $y$ coordinate of obstacles. The last line contains the instructions for the tank and the number of instructions is at least one.

• $0 \lt N, M, L, W \lt 500$
• $0 \leq O \lt N \times M - L \times W$

## Output Format

Print the current map information if the instruction is $0$.

## Sample Input 1

5 5 1 142 12 34 14 42 1 4 3 1 2 2 2 2 1 1 1 0


## Sample Output 1

0000000202000000020000001


## Sample Input 2

4 5 2 360 21 21 32 33 04 20 2 0 1 3 2 0


## Sample Output 2

111201110022002022001112011100220020220011100111002200202200


## Sample Input 3

4 5 2 360 21 21 32 33 04 20 5 4 0 5 1 3 2 0


## Sample Output 3

111201110022002022000111001110200020220000000011102111002200