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D - Arrays and Palindrome /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 数列 a に含まれる数の総和は N である。
• 数列 b に含まれる数の総和は N である。
• 数列 a, b に含まれる数はすべて正の整数である。
• 以下の条件を 2 つとも満たす長さ N の文字列は、必ずすべての文字が同じである。
• 先頭の a_1 文字、続く a_2 文字、さらに続く a_3 文字 ... はすべて回文である。
• 先頭の b_1 文字、続く b_2 文字、さらに続く b_3 文字 ... はすべて回文である。

しかしある日、高橋君は数列 a, b を両方ともなくしてしまいました。 幸運なことに、高橋君は数列 a が長さ M の数列 A の並び替えであったことを覚えています。

### 制約

• 1≦N≦10^5
• 1≦M≦100
• 1≦A_i≦10^5
• A_i の総和は N である。

### 入力

N M
A_1 A_2 ... A_M


### 入力例 1

3 2
2 1


### 出力例 1

1 2
1
3


### 入力例 2

6 1
6


### 出力例 2

6
3
1 2 3


### 入力例 3

55 10
1 2 3 4 5 6 7 8 9 10


### 出力例 3

Impossible


Score : 1000 points

### Problem Statement

Snuke got a present from his mother on his birthday. The present was a pair of two sequences a and b, consisting of positive integers. They satisfied all of the following properties:

• The sum of all elements of a is N.
• The sum of all elements of b is N.
• Any string of length N that satisfies the following two conditions (1) and (2) will also satisfy the condition (3).
• (1) Any of the following forms a palindrome: the first a_1 letters, the following a_2 letters, the following a_3 letters and so on.
• (2) Any of the following forms a palindrome: the first b_1 letters, the following b_2 letters, the following b_3 letters and so on.
• (3) All N letters are the same.

He was happy, until one day he lost both of the sequences. Now, he only remembers that the sequence a was a permutation of another sequence A of length M.

To bring him happiness again, his mother has decided to give him another pair of sequences a and b that satisfies his favorite properties and is consistent with his memory.

### Constraints

• 1≦N≦10^5
• 1≦M≦100
• 1≦A_i≦10^5
• The sum of all A_i equals N.

### Input

The input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M


### Output

If there exists a pair of sequences a and b that satisfies the properties and is consistent with Snuke's memory, print three lines. The first line must contain the sequence a, the second line must contain the length of the sequence b, and the third line must contain the sequence b.

If such a pair does not exist (because Snuke's memory is wrong or some other reason), print a single line containing the word Impossible (case-sensitive).

### Sample Input 1

3 2
2 1


### Sample Output 1

1 2
1
3


### Sample Input 2

6 1
6


### Sample Output 2

6
3
1 2 3


### Sample Input 3

55 10
1 2 3 4 5 6 7 8 9 10


### Sample Output 3

Impossible