Problem A. My Faulty Touch Screen II
Problem
Just as I get used to playing the mini computer game using my faulty touch screen, the behaviour of my touch screen changes again. The mini computer game, when played with my faulty touch screen, essentially has the following rule: The game board is an m x n grid. Initially some cells are black and the others are white. The goal of the game is to turn the whole grid black. The only operation allowed is touching a cell on the the grid. When the player touches a cell on the grid, the colors of up to four cells are flipped. They are the cell being touched, the cell on the left, the cell on the right and the cell above, as shown on the diagram below. Of course, if some of those cells are not on the grid (e.g. I pick the cell at the top right corner), the colors of less than four cells will be flipped.
I find it really hard to solve some of the puzzles. I strongly suspect that these puzzles are unsolvable. Moreover, I found that I have always finished the games for some certain grid sizes. I strongly suspect that puzzles of such grid sizes are always solvable. I can set the grid size so that the puzzles randomly generated can always be solved, but I have to find out such grid sizes first.
Input
The input starts with the number of grid sizes s. s grid sizes follow. Each grid size consists of the number of rows and number of columns. All input numbers are less than 231 - 1.
Output
For each grid size, print "Yes" if puzzles of the grid size must be solvable. Print "No" otherwise. For example, the output for the grid size 2x2 is "No" because the puzzle is unsolvable if all the cells are initially white.
Sample Input
2
3 3
2 2
Sample output
Yes
No
Author
Louis Siu