github.com/captn3m0/codechef.git

---
category_name: medium
problem_code: ANUBTT
problem_name: 'Build the Tree'
languages_supported:
    - ADA
    - ASM
    - BASH
    - BF
    - C
    - 'C99 strict'
    - CAML
    - CLOJ
    - CLPS
    - 'CPP 4.3.2'
    - 'CPP 4.9.2'
    - CPP14
    - CS2
    - D
    - ERL
    - FORT
    - FS
    - GO
    - HASK
    - ICK
    - ICON
    - JAVA
    - JS
    - 'LISP clisp'
    - 'LISP sbcl'
    - LUA
    - NEM
    - NICE
    - NODEJS
    - 'PAS fpc'
    - 'PAS gpc'
    - PERL
    - PERL6
    - PHP
    - PIKE
    - PRLG
    - PYTH
    - 'PYTH 3.4'
    - RUBY
    - SCALA
    - 'SCM guile'
    - 'SCM qobi'
    - ST
    - TCL
    - TEXT
    - WSPC
max_timelimit: '4'
source_sizelimit: '50000'
problem_author: anudeep2011
problem_tester: gerald
date_added: 22-04-2014
tags:
    - anudeep2011
    - cook46
    - hard
    - min
editorial_url: 'http://discuss.codechef.com/problems/ANUBTT'
time:
    view_start_date: 1400437800
    submit_start_date: 1400437800
    visible_start_date: 1400437800
    end_date: 1735669800
    current: 1493557470
layout: problem
---
All submissions for this problem are available.###  Read problems statements in [Mandarin Chinese](http://www.codechef.com/download/translated/COOK46/mandarin/ANUBTT.pdf) and [Russian](http://www.codechef.com/download/translated/COOK46/russian/ANUBTT.pdf) as well.

### 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**. **N-1** 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

<pre><b>Input:</b>
3
2 2 3
1 2
2 3
2
2 2 10
10 10
3 2 10
1 2 2

<b>Output:</b>
40
6
</pre>### 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./>/>/>/>