SP2853 PDECODE - Decode the Strings

Bruce Force has had an interesting idea how to encode strings. The following is the description of how the encoding is done: Let x $ _{1} $ ,x $ _{2} $ ,...,x $ _{n} $ be the sequence of characters of the string to be encoded. 1. Choose an integer _m_ and _n_ pairwise distinct numbers p $ _{1} $ ,p $ _{2} $ ,...,p $ _{n} $ 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 y $ _{i} $ to x $ _{pi} $ , and then for _1_ ≤ i ≤ _n_ replace x $ _{i} $ by y $ _{i} $ . 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 p $ _{1} $ , ..., p $ _{n} $ 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?

The input contains several test cases. Each test case starts with a line containing two numbers _n_ and _m_ (_1 ≤ n ≤ 80_, _1 ≤ m ≤ 10 $ ^{9} $_ ). The following line consists of _n_ pairwise different numbers p $ _{1} $ ,...,p $ _{n} $ (_1_ ≤ p $ _{i} $ ≤ _n_). 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.

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