| You're throwing a party for your friends, but since your friends may not all |
| know each other, you're afraid a few of them may not enjoy your party. So to |
| avoid this situation, you decide that you'll also invite some friends of your |
| friends. But who should you invite to throw a great party? |
|
|
| Luckily, you are in possession of data about all the friendships of your |
| friends and their friends. In graph theory terminology, you have a subset |
| **G** of the social graph, whose vertices correspond to your friends and their |
| friends (excluding yourself), and edges in this graph denote mutual |
| friendships. Furthermore, you have managed to obtain exact estimates of how |
| much food each person in **G** will consume during the party if he were to be |
| invited. |
|
|
| You want to choose a set of guests from **G**. This set of guests should |
| include all your friends, and the subgraph of **G** formed by the guests must |
| be connected. You believe that this will ensure that all of your friends will |
| enjoy your party since any two of them will have something to talk about... |
|
|
| In order to save money, you want to pick the set of guests so that the total |
| amount of food needed is as small as possible. If there are several ways of |
| doing this, you prefer one with the fewest number of guests. |
|
|
| The people/vertices in your subset **G** of the social graph are numbered from |
| 0 to **N** \- 1. Also, for convenience your friends are numbered from 0 to |
| **F** \- 1, where **F** is the number of your friends that you want to invite. |
| You may also assume that **G** is connected. Note again that you are not |
| yourself represented in **G**. |
|
|
| ## Input |
|
|
| The first line of the input consists of a single number **T**, the number of |
| test cases. Each test case starts with a line containing three integers **N**, |
| the number of nodes in **G**, **F**, the number of friends, and **M**, the |
| number of edges in **G**. This is followed by **M** lines each containing two |
| integers. The **i**th of these lines will contain two distinct integers **u** |
| and **v** which indicates a mutual friendship between person **u** and person |
| **v**. After this follows a single line containing **N** space-separated |
| integers with the **i**th representing the amount of food consumed by person |
| **i**. |
| |
|
|
| ## Output |
|
|
| Output **T** lines, with the answer to each test case on a single line by |
| itself. Each line should contain two numbers, the first being the minimum |
| total quantity of food consumed at a party satisfying the given criteria and |
| the second the minimum number of people you can have at such a party. |
| |
|
|
| ## Constraints |
|
|
| **T** = 50 |
| 1 ≤ **F** ≤ 11 |
| **F** ≤ **N**-1 |
| 2 ≤ **N** ≤ 250 |
| **N**-1 ≤ **M** ≤ **N** * (**N** \- 1) / 2 |
| **G** is connected, and contains no self-loops or duplicate edges. |
| For each person, the amount of food consumed is an integer between 0 and 1000, |
| both inclusive. |
|
|
|
|
