You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
There are two water tanks, the first one fits $$$a$$$ liters of water, the second one fits $$$b$$$ liters of water. The first tank has $$$c$$$ ($$$0 \le c \le a$$$) liters of water initially, the second tank has $$$d$$$ ($$$0 \le d \le b$$$) liters of water initially.

You want to perform $$$n$$$ operations on them. The $$$i$$$-th operation is specified by a single non-zero integer $$$v_i$$$. If $$$v_i > 0$$$, then you try to pour $$$v_i$$$ liters of water from the first tank into the second one. If $$$v_i < 0$$$, you try to pour $$$-v_i$$$ liters of water from the second tank to the first one.

When you try to pour $$$x$$$ liters of water from the tank that has $$$y$$$ liters currently available to the tank that can fit $$$z$$$ more liters of water, the operation only moves $$$\min(x, y, z)$$$ liters of water.

For all pairs of the initial volumes of water $$$(c, d)$$$ such that $$$0 \le c \le a$$$ and $$$0 \le d \le b$$$, calculate the volume of water in the first tank after all operations are performed.

## Input Format
The first line contains three integers $$$n, a$$$ and $$$b$$$ ($$$1 \le n \le 10^4$$$; $$$1 \le a, b \le 1000$$$) — the number of operations and the capacities of the tanks, respectively.

The second line contains $$$n$$$ integers $$$v_1, v_2, \dots, v_n$$$ ($$$-1000 \le v_i \le 1000$$$; $$$v_i \neq 0$$$) — the volume of water you try to pour in each operation.

## Output Format
For all pairs of the initial volumes of water $$$(c, d)$$$ such that $$$0 \le c \le a$$$ and $$$0 \le d \le b$$$, calculate the volume of water in the first tank after all operations are performed.

Print $$$a + 1$$$ lines, each line should contain $$$b + 1$$$ integers. The $$$j$$$-th value in the $$$i$$$-th line should be equal to the answer for $$$c = i - 1$$$ and $$$d = j - 1$$$.

## Examples
```input
3 4 4
-2 1 2
```
```output
0 0 0 0 0 
0 0 0 0 1 
0 0 1 1 2 
0 1 1 2 3 
1 1 2 3 4
```
-----
```input
3 9 5
1 -2 2
```
```output
0 0 0 0 0 0 
0 0 0 0 0 1 
0 1 1 1 1 2 
1 2 2 2 2 3 
2 3 3 3 3 4 
3 4 4 4 4 5 
4 5 5 5 5 6 
5 6 6 6 6 7 
6 7 7 7 7 8 
7 7 7 7 8 9
```

## Note
Consider $$$c = 3$$$ and $$$d = 2$$$ from the first example:

- The first operation tries to move $$$2$$$ liters of water from the second tank to the first one, the second tank has $$$2$$$ liters available, the first tank can fit $$$1$$$ more liter. Thus, $$$\min(2, 2, 1) = 1$$$ liter is moved, the first tank now contains $$$4$$$ liters, the second tank now contains $$$1$$$ liter.
- The second operation tries to move $$$1$$$ liter of water from the first tank to the second one. $$$\min(1, 4, 3) = 1$$$ liter is moved, the first tank now contains $$$3$$$ liters, the second tank now contains $$$2$$$ liter.
- The third operation tries to move $$$2$$$ liter of water from the first tank to the second one. $$$\min(2, 3, 2) = 2$$$ liters are moved, the first tank now contains $$$1$$$ liter, the second tank now contains $$$4$$$ liters.

There's $$$1$$$ liter of water in the first tank at the end. Thus, the third value in the fourth row is $$$1$$$.

Now solve the problem and return the code.