H - Shuffling Machine
Editorial
/

KM bought a new card shuffling machine.

According to his hypothesis, everytime you setup

He wanted to know this sequence, so he setup

But KM says that you can guess

The first line of the input file contains the integers

The second line of the input file contains N different integers which denotes

If KM's hypothesis seems to be wrong, just print

Time Limit: 1.5 sec / Memory Limit: 93 MB

### Description

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

`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

`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