Xor Travellers

There are $K$ travellers who want to travel through a country one after the other. The country is in the form of a $2$-d grid and is divided into $N$ rows and $M$ columns, such that each cell of the grid can be considered to be a city. Each city is initially marked with either 0 or 1. Let city $(i,j)$ (the city at the intersection of the $i^{th}$ row and $j^{th}$ column) be marked with number $C