Japan Alumni Group Summer Camp 2013 Warming Up

H - Shuffling Machine


Time limit時間制限 : 1.5sec / Memory limitメモリ制限 : 96MB

Description

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?

Input

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.

Output

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.

Sample Input

3 2
3 1 2

Sample Output

2 3 1

Sample Input

3 2
1 3 2

Sample Output

Impossible

Sample Input

4 2
2 1 4 3

Sample Output

Ambiguous

Source name

The First KMCMonthly Contest

Submit提出する