A permutation of the set { 1, 2, … , n} is a way to sort those numbers. For instance, [123], [132], [213], [231], [312], and [321] are the 6 possible permutations for n = 3.

An alternative way to describe a permutation is giving its cycles. For instance, the permutation [6351274] can be written (1 6 7 4) (2 3 5). This is, to the position 1 goes the 6, to the position 6 goes the 7, to the position 7 goes the 4, to the position 4 goes the 1 (first cycle), to the position 2 goes the 3, to the position 3 goes the 5, and to the position 5 goes the 2 (second cycle). Notice that there are various ways to describe a permutation using cycles. For instance, the last permutation can be written also as (3 5 2) (6 7 4 1).

As can be seen on the right, the same permutation can be applied repeatedly. Thus, applying twice [6351274] [7526341] = (7 1) (6 4) (5 3 2) is obtained.

After three times we have [4237516] = (4 7 6 1) (2) (3) (5), and after 4 times [1364267] = (1) (4) (6) (7) (3 5 2). It is easy to see than after 12 times [1234567] = (1) (2) (3) (4) (5) (6) (7) would be obtained.

Your task is to write a program that, for each given permutation, prints the result to apply it a certain number of times.

Input

The input consists of a sequence of cases. Each case starts with a line with n, c, and m (respectively, the number of elements of the permutation, its number of cycles, and the number of tests). c lines follow, one per cycle. Each cycle follows exactly the format of the instances. Then, m lines come, each one with k (the number of times that the permutation must be applied). You can assume 1 ≤ n ≤ 10000, 1 ≤ c ≤ n, m ≥ 1, and k ≥ 1.

Output

For each case of the input, your program must print the permutation obtained after applying k times the given permutation. It must print a line in white in the end of the answers for each case. Follow the format of the instances.

- (25 points)
- (20 points) Some test cases will exclusively contain cases like the ones in the instance of input 2, in which all the k ≤ 100.
- (55 points)
Other test cases will contain cases of every kind,
in which k ≤ 10
^{9}.

Scoring

- TestA: 25 Points
Some test cases will exclusively contain cases like the ones in the instances of input 1, in which all the k are 1.

- TestB: 20 Points
Some test cases will exclusively contain cases like the ones in the instance of input 2, in which all the k ≤ 100.

- TestC: 55 Points
Other test cases will contain cases of every kind, in which k ≤ 10

^{9}.

Public test cases

**Input**

7 2 3 (1 6 7 4) (2 3 5) 1 1 1 4 4 1 (1) (4) (2) (3) 1

**Output**

6 3 5 1 2 7 4 6 3 5 1 2 7 4 6 3 5 1 2 7 4 1 2 3 4

**Input**

7 2 8 (1 6 7 4) (2 3 5) 1 2 3 4 12 16 20 24 4 1 3 (2 3 4 1) 1 2 100

**Output**

6 3 5 1 2 7 4 7 5 2 6 3 4 1 4 2 3 7 5 1 6 1 3 5 4 2 6 7 1 2 3 4 5 6 7 1 3 5 4 2 6 7 1 5 2 4 3 6 7 1 2 3 4 5 6 7 2 3 4 1 3 4 1 2 1 2 3 4

**Input**

7 2 1 (3 5 2) (6 7 4 1) 1000000000

**Output**

1 3 5 4 2 6 7

Information

- Author
- Omer Giménez
- Language
- English
- Translator
- Carlos Molina
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++