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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 $$(4,\;5)$$.