Permutations P90339

A permutation of the set $\{ 1, 2, \dots , n\}$ 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 $1 \le n \le 10000$, $1 \le c \le n$, $m \ge 1$, and $k \ge 1$.

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.

Score

• (25 points)

• (20 points) Some test cases will exclusively contain cases like the ones in the instance of input 2, in which all the $k \le 100$.

• (55 points) Other test cases will contain cases of every kind, in which $k \le 10^9$.

Scoring

• TestA:

  Some test cases will exclusively contain cases like the ones in the instances of input 1, in which all the $k$ are 1.

• TestB:

  Some test cases will exclusively contain cases like the ones in the instance of input 2, in which all the $k \le 100$.

• TestC:

  Other test cases will contain cases of every kind, in which $k \le 10^9$.