AT_icpc2013summer_warmingUp_h Shuffling Machine

[problemUrl]: https://atcoder.jp/contests/jag2013summer-warmingup/tasks/icpc2013summer_warmingUp_h KM bought a new card shuffling machine. According to his hypothesis, everytime you setup $ N $ cards and push the switch, it shuffles the cards in a totally same way. More precisely, there exists a sequence of integers $ a_1 $, $ a_2 $, ..., $ a_N $ such that - the 1st card in the resulting order is always the $ a_1 $-th card in the initial order, - the 2nd card in the resulting order is always the $ a_2 $-th card in the initial order, - ..., and so on. He wanted to know this sequence, so he setup $ N $ cards in the ascending order: $ 1 $, $ 2 $, ..., $ N $. However, he accidentally pushed the switch $ K $ times, and the resulting order of the cards was $ b_1 $, $ b_2 $, ..., $ b_N $. But KM says that you can guess $ a_1 $, $ a_2 $, ..., $ a_N $ from $ b_1 $, $ b_2 $, ..., $ b_N $. Can you do that? The first line of the input file contains the integers $ N $ ($ 1\ \leq\ N\ \leq\ 10^5 $) and $ K $ ($ 1\ \leq\ K\ \leq\ 10^{18} $), separated by a space. The second line of the input file contains N different integers which denotes $ b_1 $, $ b_2 $, ..., $ b_N $ ($ 1\ \leq\ b_i\ \leq\ N $) in this order, separated by a space. If KM's hypothesis seems to be wrong, just print `Impossible`. If there are several possibilities, print `Ambiguous`. Otherwise, print $ N $ integers which denotes $ a_1 $, $ a_2 $, ..., $ a_N $ in this order, separated by a space. ``` 3 2 3 1 2 ``` ``` 2 3 1 ``` ``` 3 2 1 3 2 ``` ``` Impossible ``` ``` 4 2 2 1 4 3 ``` ``` Ambiguous ```

N/A

N/A