For nodes of degree $$$2$$$, the sum of labels on the edges is always $$$k$$$, so we need to find a way to differentiate between the two types of nodes (all edges pointing outwards or all edges pointing inwards).

Consider adding $$$k+1$$$ to the labels of edges at depth congruent to $$$0$$$ or $$$1 \pmod 4$$$. Notice that a degree $$$2$$$ node has its adjacent edges pointing towards it if and only if it has an even number of adjacent edges that have label $$$\geq k+1$$$. Now that we can figure out the parity of the depth of a degree $$$2$$$ node based on the labels, we can proceed with the same solution as subtasks 3 and 4.