Build the Tree

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Problem description.
Given a rooted tree with N nodes. Nodes of the tree are numbered from 1 to N. Node 1 is the root. You need to add M nodes to it in the given order. All the nodes have values. Cost for adding a node A with value va to another node B with value vb is va*vb. There is an additional cost of y (so total cost of va*vb+y) if B has atleast x child nodes. After node A has been added to another node B it becomes a child of B.
After adding a node A to the tree, nodes next in list can be added to A also. You need to calculate the total minimal cost to add all M nodes in given order.
Input
The first line of input contains N. The second line of input contains N integers representing the values of nodes in order from node 1 to node N. N1 lines follow, each line defines an edge. Each line has 2 integers, which says that those 2 nodes are connected.
Next line of input contains an integer Q, denoting the number of queries you need to answer. Each query consists of 2 lines. The first line of each query has 3 integers, M x y. The second line of each query has M integers representing the values of the nodes to be added in order.
Note that in each query, M nodes are added to the initial tree, and hence changes made in previous query should not be considered in later queries
Output
For each query, output a single line containing the minimal total cost to add all the nodes in given order.
Constraints
 1 ≤ N ≤ 100000
 1 ≤ x ≤ 1000
 1 ≤ y ≤ 1000
 1 ≤ Q ≤ 100
 1 ≤ M ≤ 100
 1 ≤ Values of all nodes in input ≤ 1000
Example
Input: 3 2 2 3 1 2 2 3 2 2 2 10 10 10 3 2 10 1 2 2 Output: 40 6
Explanation
Query 1.
Optimal solution is to add the first node from the query to node 1 of the tree and the second node from the query to node 2 of the tree. Cost is 10*2 + 10*2.
Query 2.
Optimal solution is to add the first node from the query to node 1 of the tree for a cost 2. Then add next two nodes from the query to newly added node.
Total cost is 2 + 2 + 2 = 6.
Author:  anudeep2011 
Tester:  gerald 
Editorial  http://discuss.codechef.com/problems/ANUBTT 
Tags  anudeep2011, cook46, hard, mincostflow 
Date Added:  22042014 
Time Limit:  4 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, PYP3, CLOJ, FS 
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