The Matrix Game

Two players A and B play the following game. 1) First, a matrix M of size N*M is chosen, and filled with non-zero numbers. 2) Player A starts the game and the players play alternately. 3) In his turn, a player chooses any row which has atleast one non zero number in it. In this row, the leftmost non zero number is chosen. Let this number be K. The player subtracts any number between 1 and K inc