1735: 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 x₁,x₂,...,x_n be the sequence of characters of the string to be encoded. 1. Choose an integer m and n pairwise distinct numbers p₁,p₂,...,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 p₁, ..., 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 ≤ 10⁹). The following line consists of n pairwise different numbers p₁,...,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.

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?