Optimal separation

Consider the sequence $1, 2, \dots, n$ . If we use $k$ separators among those numbers, we get $k + 1$ subsequences. Let $s_i$ be the sum of the elements of the $i$ -th subsequence. Let $m$ be the minimum $s_i$ , and let $M$ be the maximum $s_i$ . Given $n$ and $k$ , please choose where to place the $k$ separators so that $M - m$ is as small as possible.

Input

Input consists of several cases, each one with $n$ and $k$ . You can assume $1 \le n \le 50$ and $0 \le k \le \min(n - 1, 10)$ .

Output

For every case, print $k + 3$ lines. On the first line print the minimum $M - m$ . Afterwards, print a line for each of the $k + 1$ subsequences, in order, with the numbers and their sum. Finally, print a line with 10 dashes. Follow exactly the format of the sample output. If there is more than one optimal solution, choose any one.

Observation

The expected solution is a dynamic programming. This problem could also be solved by precomputing the solutions. But, if you do that, your solution will be manually rejected.

Problem information

Author: Josep Grané

Generation: 2026-01-25T11:04:18.924Z