24 Matchstick Puzzle

Consider a 3×3 grid puzzle made from 24 matchsticks. At first, every matchstick is placed as follows.

+--+--+--+
|..|..|..|
|..|..|..|
+--+--+--+
|..|..|..|
|..|..|..|
+--+--+--+
|..|..|..|
|..|..|..|
+--+--+--+

Two consecutive - characters represent one horizontal matchstick, and two consecutive | characters represent one vertical matchstick. A + marks a point where matchstick endpoints can meet, and . marks empty space.

Initially, the grid contains 14 squares: nine 1×1 squares, four 2×2 squares, and one 3×3 square.

You are given integers N and K. Remove exactly N matchsticks so that all of the following conditions hold.

• Exactly N matchsticks are removed.
• The remaining grid contains exactly K completed squares.
• Every remaining matchstick is used as a side of at least one completed square.

Write a program that prints one grid satisfying these conditions.

The first line contains integers N and K. (1 ≤ N < 24, 1 ≤ K < 14)

N is the number of matchsticks to remove, and K is the number of squares that must remain.

Print a grid satisfying the conditions in 10 lines.

1. Print + at every point where matchstick endpoints can meet, even if no matchstick touches that point.
2. Print . at every position where no matchstick is placed.
3. Print one horizontal matchstick as two consecutive - characters.
4. Print one vertical matchstick as two consecutive | characters.

Every input is guaranteed to have at least one valid answer. If there are multiple valid grids, you may print any one of them.