B. Corner Twist

You are given two grids of numbers 𝑎 and 𝑏, with 𝑛 rows and 𝑚 columns. All the values in the grid are 0, 1 or 2.

You can perform the following operation on 𝑎 any number of times:

• Pick any subrectangle in the grid with length and width ≥2. You are allowed to choose the entire grid as a subrectangle.
• The subrectangle has four corners. Take any pair of diagonally opposite corners of the chosen subrectangle and add 1 to their values modulo 3.
• For the pair of corners not picked, add 2 to their values modulo 3.

Note that the operation only changes the values of the corners of the picked subrectangle.

Is it possible to convert the grid 𝑎 into grid 𝑏 by applying the above operation any number of times (possibly zero)?