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