Tree Infection

You are given a rooted tree consisting of $N$ vertices, along with integers $R$ and $M$. The vertices are numbered from $1$ to $N$, with vertex $1$ as a root. Each of the other vertices has a single parent in the tree.

If a vertex s is chosen, it becomes infected along with all its descendants (i.e. vertices that can be reached by following edges downward from s) at a distance of $R$ or less, where distance is calculated as the number of edges between vertices. A vertex $u$ is considered reachable from vertex $v$ if and only if neither of them is infected, and the number of infected vertices on the path between them does not exceed $M$.

For each possible chosen vertex $s$ ($1 ≤ s ≤ N$), you must calculate the number of vertex pairs $(u, v)$ such that $1 ≤ u < v ≤ N$ and $u$ is reachable from $v$ (and vice versa).

The first line contains three integers: $N$, $R$ and $M$.

The second line contains $N - 1$ integers: $p[2]$, $p[3]$, $\dots$, $p[N]$, the parents of the vertices $2$, $3$, $\dots$,$N$, respectively.

Print $N$ lines with single integer each: $s$-th line should contain required number of pairs when the chosen vertex is $s$.

It's not recommended to use std::endl for outputting newline symbols. Instead, consider using '\n' for better performance.

• $2 ≤ N ≤ 500\,000$
• $1 ≤ p[i] < i$ (for each $2 ≤ i ≤ N$)
• $0 ≤ R ≤ N - 1$
• $0 ≤ M ≤ 2 \times R + 1$