Two Tanks

Description:

Input:

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:

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 $$$d = j - 1$$$.

Sample Input:

3 4 4
-2 1 2

Sample 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 

Sample Input:

3 9 5
1 -2 2

Sample 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 $$$1$$$.