P11358 [eJOI 2023] Tree Infection

You are given a rooted tree $T$ with $N$ nodes, where the root is guaranteed to be node $1$. A node $s$ on the tree will be chosen. All nodes whose distance to $s$ is **not greater than** $R$ will be infected, where the distance between two nodes is defined as the number of edges on the path between them in the tree. A pair of nodes is reachable if and only if both nodes are not infected, and the number of infected nodes on the path between them is **not greater than** $M$. For $s=1,2,\cdots,N$, compute the number of reachable pairs of nodes when choosing $s$.

The first line contains three integers $N,R,M$. The second line contains $N-1$ integers $p_2,p_3,\cdots,p_N$, representing the parent of each node.

Output $N$ lines, each containing one integer. The integer on line $s$ represents the answer when choosing $s$.

**[Sample Explanation]**  The tree for $s=2$ is shown in the figure. All reachable pairs are $(1,13)$, $(7,8)$, $(7,9)$, and $(8,9)$. Note that $(1,2)$ is not reachable because $2$ is already infected; $(1,5)$ is not reachable because there are three infected nodes $2,3,4$ on the path. **[Constraints]** **This problem uses bundled tests.** - Subtask 1 (20 pts): $N\leq 300$. - Subtask 2 (14 pts): $R=0$. - Subtask 3 (15 pts): $M=2R+1$. - Subtask 4 (10 pts): $M=2R-1$. - Subtask 5 (16 pts): $N\leq 5\times 10^3$. - Subtask 6 (25 pts): No special constraints. For $100\%$ of the testdata, it is guaranteed that $2\leq N\leq 5\times 10^5$, $1\leq p_i