Qualification Round 2013


  Submissions
Tic-Tac-Toe-Tomek
10pt
Not attempted
19860/21861 users correct (91%)
20pt
Not attempted
16122/19755 users correct (82%)
Lawnmower
10pt
Not attempted
12579/14509 users correct (87%)
30pt
Not attempted
10569/12136 users correct (87%)
Fair and Square
10pt
Not attempted
17569/18199 users correct (97%)
35pt
Not attempted
6080/15270 users correct (40%)
55pt
Not attempted
872/3725 users correct (23%)
Treasure
20pt
Not attempted
1359/4458 users correct (30%)
60pt
Not attempted
141/547 users correct (26%)
  Top Scores
netkuba250
pieguy250
tanakh250
cgy4ever250
STEP4250
Xhark250
Balajiganapathi250
Sohel250
krijgertje250
LoRdTaPaKaH250
Practice Mode

Problem D. Treasure

This contest is open for practice. You can try every problem as many times as you like, though we won't keep track of which problems you solve. Read the Quick-Start Guide to get started.
Small input
20 points
Large input
60 points

Problem

Following an old map, you have stumbled upon the Dread Pirate Larry's secret treasure trove!

The treasure trove consists of N locked chests, each of which can only be opened by a key of a specific type. Furthermore, once a key is used to open a chest, it can never be used again. Inside every chest, you will of course find lots of treasure, and you might also find one or more keys that you can use to open other chests. A chest may contain multiple keys of the same type, and you may hold any number of keys.

You already have at least one key and your map says what other keys can be found inside the various chests. With all this information, can you figure out how to unlock all the chests?

For example, suppose the treasure trove consists of four chests as described below, and you began with exactly one key of type 1:

Chest Number  |  Key Type To Open Chest  |  Key Types Inside
--------------+--------------------------+------------------
1             |  1                       |  None
2             |  1                       |  1, 3
3             |  2                       |  None
4             |  3                       |  2
You can open all the chests in this example if you do them in the order 2, 1, 4, 3. If you start by opening chest #1 first, then you will have used up your only key, and you will be stuck.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a single line containing two positive integers K and N, representing the number of keys you start with and the number of chests you need to open.

This is followed by a line containing K integers, representing the types of the keys that you start with.

After that, there will be N lines, each representing a single chest. Each line will begin with integers Ti and Ki, indicating the key type needed to open the chest and the number of keys inside the chest. These two integers will be followed by Ki more integers, indicating the types of the keys contained within the chest.

Output

For each test case, output one line containing "Case #x: C1 C2 ... CN", where x is the case number (starting from 1), and where Ci represents the index (starting from 1) of the ith chest that you should open.

If there are multiple ways of opening all the chests, choose the "lexicographically smallest" way. In other words, you should choose to make C1 as small as possible, and if there are multiple ways of making C1 as small as possible, choose the one that makes C2 as small as possible, and so on.

If there is no way to open all the chests, you should instead output one line containing "Case #x: IMPOSSIBLE".

Limits

1 ≤ T ≤ 25.
1 ≤ K.
All key types will be integers between 1 and 200 inclusive.

Small dataset

1 ≤ N ≤ 20.
In each test case, there will be at most 40 keys altogether.

Large dataset

1 ≤ N ≤ 200.
In each test case, there will be at most 400 keys altogether.

Sample


Input
 

Output
 
3
1 4
1
1 0
1 2 1 3
2 0
3 1 2
3 3
1 1 1
1 0
1 0
1 0
1 1
2
1 1 1
Case #1: 2 1 4 3
Case #2: 1 2 3
Case #3: IMPOSSIBLE

Overview  |  Problem A  |  Problem B  |  Problem C  |  Problem D

Google Code Jam 2013 is off and running! We have 17059 advancers out of 21962 people who correctly solved at least one input, and 45754 registrants. All those numbers are records for us!

We started with Tomek's variation on a game for children (who is this Tomek anyway?!), and then quickly delved into the riddles of lawnmowers, palindromes, and pirates. Overall, it was a pretty tough set this year, with problem D in particular being something that could have been a Finals problem. A huge congratulations to the 63 people who managed to solve everything!

There are three more rounds to go before the Finals, and we're just getting started. We hope to see all the advancers in the First Rounds!


Cast

Problem A. Tic-Tac-Toe-Tomek Written by Tomek Kulczyński and Bartholomew Furrow. Prepared by Onufry Wojtaszczyk and Bartholomew Furrow.

Problem B. Lawnmower Written by Onufry Wojtaszczyk. Prepared by Jan Kuipers and Onufry Wojtaszczyk.

Problem C. Fair and Square Written by Onufry Wojtaszczyk. Prepared by Nikolay Kurtov and Onufry Wojtaszczyk.

Problem D. Treasure Written by David Arthur. Prepared by Tomek Kulczyński and David Arthur.

Contest analysis presented by Onufry Wojtaszczyk and David Arthur. Solutions and other problem preparation by Igor Naverniouk, Tomek Czajka, Karim Nosseir, Hao Pan, and Petr Mitrichev.
You cannot ask questions at this time. Please email us at codejam@google.com.
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