A15790 | Two Tanks

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.

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.

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 $d = j - 1$ .