CF217E Alien DNA

Professor Bajtocy is conducting experiments on alien DNA. He has discovered that it is subject to repetitive mutations — each mutation happens in the same way: some continuous subsequence of the alien DNA becomes active, copies itself, the copy gets mangled and inserts itself right after the original subsequence. The mangled copy of the activated continuous subsequence is formed by first joining all the elements at the even positions in that subsequence, and then joining all the elements at the odd ones at the end. That is, if the activated subsequence consists of 11 elements and represented as $ s_{1}s_{2}...\ s_{11} $ , its mangled copy is $ s_{2}s_{4}s_{6}s_{8}s_{10}s_{1}s_{3}s_{5}s_{7}s_{9}s_{11} $ . For example, if the original sequence was "ACTGG" and the mutation happened on the segment $ [2,4] $ (that is the activated subsequence is "CTG"), the mutated DNA is: "ACTGTCGG". The mangled copy of the activated subsequence is marked with bold font. Professor Bajtocy has written down the original DNA sequence and the mutations that sequentially happened to it, and he now asks you to recover the first $ k $ elements of the DNA sequence after all the mutations.

The first line of input contains the original DNA sequence, consisting only of letters "A", "C", "T" and "G" and not exceeding $ 3·10^{6} $ in length. The second line contains a single integer $ k $ ( $ 1

Output a single line, containing the first $ k $ letters of the mutated DNA sequence.

In the second example, after the first mutation the sequence is "ACCAGTACGT". After the second mutation it's "ACCAGTACCGACATCGT".