SOLVE
LATER
Monk is struggling with a problem on graph and needs your help.
Given an undirected graph of N nodes and \(N-1\) edges. There is a unique path from any node to any other node. For a given edge e, he needs to find number of pairs \((a,\;b)\), considering a and b as nodes of graph, such that e lies in the path between node a and node b.
Help monk for the same.
Input format:
First line of input contains two space separated integers, N \((1 \le N \le 10^5)\) and Q \((1 \le Q \le 10^5)\), denoting the number of nodes and number of queries.
Next \(N-1\) lines contain two space separated integers, a and b, each, denoting there is an edge between a and b \((1 \le a, b \le N)\). \(i^{th}\) line denotes \(i^{th}\) edge.
Next Q lines contain one integer, x \((1 \le x \le N-1)\), denoting the \(x^{th}\) edge.
Output format:
For each query, print the number of pairs of nodes \((a,\;b)\) such that \(x^{th}\) edge lies in the path between a and b.
For \(1^{st}\) query:
Number of pair such that \(1^{st}\) edge lies in the path between them are \((1,\;2)\), \((1,\;4)\), \((1,\;5)\), \((3,\;2)\), \((3,\;4)\) and \((3,\;5)\).
For \(2^{nd}\) query:
Number of pair such that \(2^{nd}\) edge lies in the path between them are \((1,\;3)\), \((2,\;3)\), \((4,\;3)\), and \((5,\;3)\).
For \(3^{rd}\) query:
Number of pair such that \(3^{rd}\) edge lies in the path between them are \((1,\;4)\), \((2,\;4)\), \((3,\;4)\), and \((5,\;4)\).
For \(4^{th}\) query:
Number of pair such that \(4^{th}\) edge lies in the path between them are \((1,\;5)\), \((2,\;5)\), \((3,\;5)\), and \((4,\;5)\).