No submission language available for this problem.

Description

Input

The first line contains two positive integer $N$ ($1 \leq N \leq 200\,000$) and $M$ ($N+1 \leq M \leq 10^{9}$), denoting the number of the elements in the first bag and the modulus, respectively.

The second line contains $N$ nonnegative integers $a_1,a_2,\ldots,a_N$ ($0 \leq a_1<a_2< \ldots< a_N<M$), the contents of the first bag.

Output

In the first line, output the cardinality $K$ of the set of residues modulo $M$ which Ajs cannot obtain.

In the second line of the output, print $K$ space-separated integers greater or equal than zero and less than $M$, which represent the residues Ajs cannot obtain. The outputs should be sorted in increasing order of magnitude. If $K$=0, do not output the second line.

Samples

2 5
3 4

1
2

4 1000000000
5 25 125 625

0

2 4
1 3

2
0 2

Note

In the first sample, the first bag and the second bag contain $\{3,4\}$ and $\{0,1,2\}$, respectively. Ajs can obtain every residue modulo $5$ except the residue $2$: $4+1 \equiv 0, \, 4+2 \equiv 1, \, 3+0 \equiv 3, \, 3+1 \equiv 4$ modulo $5$. One can check that there is no choice of elements from the first and the second bag which sum to $2$ modulo $5$.

In the second sample, the contents of the first bag are $\{5,25,125,625\}$, while the second bag contains all other nonnegative integers with at most $9$ decimal digits. Every residue modulo $1\,000\,000\,000$ can be obtained as a sum of an element in the first bag and an element in the second bag.