Key Insertion

As an employee of the Macrohard Company, you have been asked to implement a new data structure for storing integer keys.

The keys are kept in a special ordered collection that behaves like an array $A$ with infinitely many cells, numbered starting from $1$. Initially every cell is empty. The collection supports a single operation, $\text{Insert}(L, K)$, where $L$ is a cell index and $K$ is a positive integer.

$\text{Insert}(L, K)$ is defined recursively:

• If cell $A[L]$ is empty, set $A[L] \leftarrow K$.
• If cell $A[L]$ is already occupied, first perform $\text{Insert}(L+1, A[L])$, and then set $A[L] \leftarrow K$.

You are given $N$ indices $L_1, L_2, \ldots, L_N$. Starting from the empty array, perform the operations $\text{Insert}(L_1, 1)$, $\text{Insert}(L_2, 2)$, $\ldots$, $\text{Insert}(L_N, N)$ in this order, and output the final contents of the array.

The first line contains two integers $N$ and $M$: the number of Insert operations and the largest cell index that may be used in an operation ($1 \le N \le 131072$, $1 \le M \le 131072$).

The second line contains $N$ integers $L_1, L_2, \ldots, L_N$ describing the operations to perform ($1 \le L_i \le M$).

Output the contents of the array after all of the operations have been performed. On the first line, print $W$, the largest index of a non-empty cell. On the second line, print the $W$ integers $A[1], A[2], \ldots, A[W]$, using $0$ for empty cells.