Local Contest, University of Ulm Germany
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.
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?
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 ≤ pi ≤ 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.
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