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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 $N$.

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