##### Canadian Computing Competition: 2021 Stage 1, Senior #5

Your math teacher has given you an assignment involving coming up with a sequence of integers , such that for each .

The sequence must also satisfy requirements, with the one stating that the GCD (Greatest Common Divisor) of the contiguous subsequence must be equal to . Note that the GCD of a sequence of integers is the largest integer such that all the numbers in the sequence are divisible by .

Find *any* valid sequence consistent with all of these requirements, or determine that no
such sequence exists.

#### Input Specification

The first line contains two space-separated integers, and . The next lines each contain three space-separated integers, , , and .

The following table shows how the available marks are distributed.

Subtask | |||
---|---|---|---|

marks | for each | ||

marks | for each | ||

marks | for each |

Note: an additional test case worth 1 point was added to prevent unintended solutions from passing.

#### Output Specification

If no such sequence exists, output the string `Impossible`

on one line. Otherwise, on one line,
output space-separated integers, forming the sequence . If there are multiple
possible valid sequences, any valid sequence will be accepted.

#### Sample Input 1

```
2 2
1 2 2
2 2 6
```

#### Output for Sample Input 1

`4 6`

#### Explanation of Output for Sample Input 1

If and , the GCD of is and the GCD of is , as required. Please note that other outputs would also be accepted.

#### Sample Input 2

```
2 2
1 2 2
2 2 5
```

#### Output for Sample Input 2

`Impossible`

#### Explanation of Output for Sample Input 2

There exists no sequence such that the GCD of is and the GCD of is .

## Comments

Since the original data were weak, an additional test case worth 1 point was added.