Colourful Graph

You are given $K$ colours and a directed graph with $N$ nodes numbered from **1 to N** and $M$ edges (there are no self-loops and no multiple edges). You have to colour the graph in such a manner that if two nodes $u$ and $v$ are linked in such a way that there is a path from $u$ to $v$ and also from $v$ to $u$, both nodes should have the same colour. Whereas either any of the two paths or both p