URI Online Judge | 1644

Decode the Strings

Local Contest, University of Ulm DE Germany

Timelimit: 1

Bruce Force has had an interesting idea how to encode strings. The following is the description of how the encoding is done:

Let x1,x2,...,xn be the sequence of characters of the string to be encoded.

  1. Choose an integer M and N pairwise distinct numbers p1,p2,...,pn from the set {1, 2, ..., N} (a permutation of the numbers 1 to N).
  2. Repeat the following step m times.
  3. For 1 ≤ i ≤ N set yi to xpi, and then for 1 ≤ i ≤ N replace xi by yi.

For example, when we want to encode the string "hello", and we choose the value M = 3 and the permutation 2, 3, 1, 5, 4, the data would be encoded in 3 steps: "hello" -> "elhol" -> "lhelo" -> "helol".

Bruce gives you the encoded strings, and the numbers M and p1, ..., pn used to encode these strings. He claims that because he used huge numbers m for encoding, you will need a lot of time to decode the strings. Can you disprove this claim by quickly decoding the strings?

Input

The input contains several test cases. Each test case starts with a line containing two numbers N and M (1 ≤ N ≤ 80, 1 ≤ M ≤ 109). The following line consists of N pairwise different numbers p1,...,pn (1 ≤ piN). The third line of each test case consists of exactly N characters, and represent the encoded string. The last test case is followed by a line containing two zeros.

Output

For each test case, print one line with the decoded string.

Sample Input Sample Output

5 3
2 3 1 5 4
helol
16 804289384
13 10 2 7 8 1 16 12 15 6 5 14 3 4 11 9
scssoet tcaede n
8 12
5 3 4 2 1 8 6 7
encoded?
0 0

hello
second test case
encoded?