Dosun-Fuwari: an introduction

Question

^{This is an entry for Fortnightly Topic Challenge #44: Introduce a new grid deduction genre to the community.}

I'm pleased to introduce you to the Dosun-Fuwari puzzle. Rules to fill the grid (translated from an Italian magazine):

• place some anvils (A) and some balloons (B) into the grid. In each region there is exactly one anvil and exactly one balloon (the regions are are outlined with a strong border).
• since balloons are light, they float. Balloons can be placed only in the top row of the grid, under a brick (shaded cell) or under another balloon.
• since anvils are heavy, they fall down. Anvils can be placed only in the bottom row of the grid, over a brick (shaded cell) or over another anvil.

Here is an example easy grid and its solution taken from the same magazine.

Now solve this big grid:

Have fun!

Answer 1

First, we can make some obvious deductions on the bottom and bottom left. On the bottom left, we need the anvil to be in the bottom left corner and the balloon to be blocked by the wall, since if it was switched the balloon would have no anchor. (Similar logic applies for future deductions.)

Next, a few more deductions. The 2x1 at R8C7-8 region can only go one way, which helps us build the surrounding regions.

Now we flesh out the full bottom right side of the puzzle. Again, the 2x1 region at R9C4-5 has a balloon that needs an anchor, and therefore must be placed under the wall; this helps us make the other deductions.

With this, we can start to build the rest of the puzzle.

Now we have to make a stack of balloons to finish the left boxes. They can only go on the right side of the anvil stack, since if they went on the left, the bottom balloons have no anchor. This gives us the final grid: