Donald loves to play chess and often invents new pieces, making the game more interesting. Donald's chessboard is seen as a grid of $N$ lines and $M$ columns. The rows are numbered from $1$ to $N$ from top to bottom, the columns are numbered from $1$ to $M$ to the right. The intersection of row $x$ column $y$ is called cell $(x;y)$.
One day, he created a new piece by himself - piece $A$. The rule of this piece's movement is: if the piece is in cell $(x;y)$ then in the next step it can go to one of $4$ cell $(x,y+2),(x,y-2),(x-2,y)$ or $(x+2,y)$ provided that the cell is in the chessboard.
He wondered, if we put piece $A$ in cell $(x_1,y_1)$, would it be possible to move the piece to cell $(x_2,y_2)$, and if so, at least how many steps would it take for the piece to get there
This is actually an exercise using my Python computer language, but I like to think of it mathematically. I'm trying to split the cases, the first case is that $x_1$ and $y_1$ are both even, so $x_2$ and $y_2$ are both odd, so there's no way to move to this cell. Same with other cases. But I'm quite confused because I don't think the answer is that simple, please tell me if the above thought is right or wrong, and if it is wrong, please help me to solve this problem.