Puppy and Board

Tuzik and Vanya are playing the following game. They have an N × M board and a chip to indicate the current game position. The chip can be placed on any one cell of the game board, each of which is uniquely identified by an ordered pair of positive integers (r, c), where 1 ≤ r ≤ N is the row number and 1 ≤ c ≤ M is the column number. Initially, the chip is placed at the cell identified as (1, 1)