Balanced Goods Distribution

In the ancient port of Genoa, there are three kinds of goods — pottery, furniture and marble — with weights of $1$, $2$, and $3$ units respectively. In total there are $n$ goods (where $n=a+b+c$, with $a$, $b$, $c$ being the counts of pottery, furniture and marble respectively). There are also $p$ ships at Capua waiting to be loaded. Your task is to partition all the goods into $p$ piles subject to the following rules:

1. In each pile, the weights (representing a good) arranged from bottom to top must be strictly decreasing. (For example, marble (weight $3$) cannot be stacked on top of furniture or pottery.)

2. The difference between the total weights of any two piles cannot exceed $3$ units.

A valid solution always exists under the input constraints (note that since each pile can contain at most one of each type of goods, the maximum number of items in a pile is $3$, and hence $n \le 3p$). Output any one valid stacking scheme.

inputFormat

The input consists of a single line containing four integers separated by spaces:

• a: the number of pottery items (each weighing 1 unit),
• b: the number of furniture items (each weighing 2 units),
• c: the number of marble items (each weighing 3 units),
• p: the number of piles (ships).

It is guaranteed that a solution exists and that $n=a+b+c\le 3p$.

outputFormat

The output should describe a valid distribution of goods into $p$ piles. The first line should contain $p$ integers separated by spaces, where each integer represents the total weight of one pile. This is followed by $p$ lines, each line describing one pile. For each pile, list the weights of goods from bottom to top (separated by a space). Note that each pile must follow the strictly decreasing rule and the maximum difference between the total weights of any two piles must not exceed 3.

sample

3 3 3 3

6 6 6
3 2 1
3 2 1
3 2 1