Walk on Tree

You are given a tree with $N$ nodes (numbered $1$ through $N$). The tree is rooted at node $r$. For each node, find the number of walks with length $K$ from the root to this node modulo $998244353$. A *walk* from node $a$ to node $b$ with length $K$ is defined as a sequence of nodes $(u_1, u_2, \dots, u_{K+1})$, where $u_1 = a, u_{K+1} = b$ and for each valid $i$, there is an edge between nodes $