PhaseRepair

Task

You oversee $N$ Internet-of-Things devices arranged on a ring consisting of $M$ residues. Device $i$ currently shows an integer phase $A_i$ with $0 \leq A_i \lt M$. Whenever you broadcast the instruction $\text{bump residue } r$, all devices whose phase is exactly $r$ simultaneously advance to $(r + 1)\ \text{mod}\ M$. You may choose your future broadcasts after observing the new phases. Your goal is to make every device show the same phase using as few broadcasts as possible.

Input data

The input file consists of:

• a line containing integers $N, M$.
• a line containing the $N$ integers $A_0, \dots , A_{N−1}$.

Output data

The output file must contain $2$ lines:

• a line containing integer $B$: the minimum number of broadcasts required to synchronize all devices.
• a line containing $B$ integers $R_0, \dots , R_{B−1}$ describing an optimal sequence of broadcasts.

Constraints and clarifications

• $1 \leq N \leq 200\ 000$.
• $1 \leq M \leq 200\ 000$.
• $0 \leq A_i \lt M$ for every $i$.
• Note: any optimal sequence is accepted as long as the broadcasts are printed in the order they are performed.

Example 1

stdin

5 2
1 0 1 0 0

stdout

1
0

Explanation

In the first sample case, a single broadcast of residue $0$ synchronizes all devices, and broadcasting residue $1$ would also work.

Example 2

stdin

5 6
1 0 3 5 1

stdout

4
3 4 5 0

Explanation

In the second sample case, the broadcasts $3$, $4$, $5$, $0$ sweep through all occupied residues and align every device at phase $1$.

Example 3

stdin

4 4
3 3 3 3

stdout

0

Explanation

In the third sample case, every device already shows the same phase, so no broadcast is needed.