A pair of nodes, $(a,b)$, is a similar pair if the following conditions are true:

node $a$ is the ancestor of node $b$
$abs(a-b)\leq k$

Given a tree where each node is labeled from $1$ to $n$, find the number of similar pairs in the tree.

For example, given the following tree:

We have the following pairs of ancestors and dependents:

Pair abs(a-b) Pair abs(a-b)
1,2 1 3,4 1
1,3 2 3,5 2
1,4 3 3,6 3
1,5 4
1,6 5

If $k=3$ for example, we have $6$ pairs that are similar, where $abs(a-b)\leq k$.

Function Description

Complete the similarPair function in the editor below. It should return an integer that represents the number of pairs meeting the criteria.

similarPair has the following parameter(s):

n: an integer that represents the number of nodes
k: an integer
edges: a two dimensional array where each element consists of two integers that represent connected node numbers

Input Format

The first line contains two space-separated integers $n$ and $k$, the number of nodes and the similarity threshold.

Each of the next $n-1$ lines contains two space-separated integers defining an edge connecting nodes $p[i]$ and $c[i]$, where node $p[i]$ is the parent to node $c[i]$.

Constraints

$1\leq n\leq10^5$
$0\leq k\leq n$
$1\leq p[i],c[i]\leq n$

Output Format

Print a single integer denoting the number of similar pairs in the tree.

Sample Input
5 2
3 2
3 1
1 4
1 5

Sample Output
4

Explanation

The similar pairs are $(3,2)$, $(3,1)$, $(3,4)$, and $(3,5)$, so we print $4$ as our answer.

Observe that $(1,4)$ and $(1,5)$ are not similar pairs because they do not satisfy $abs(a-b)\leq k$ for $k=2$.

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