Problem Statement

$N$ teams numbered from $1$ to $N$ hold a tournament. The initial score of each team is $0$.

The tournament proceeds according to the following rules.

• In the tournament, matches are played in order, $1$ match at a time, until the termination condition described below is satisfied. In each match, exactly $1$ team among all $N$ teams becomes the "winner".
• For every 1 match, the winner gets $2$ points, and each of the $N-1$ teams that are not the winner gets $1$ point.
• A team whose score is at least $K$ immediately before the start of a match is called "ready". If a ready team becomes the winner, the tournament ends with that match as the last one, and that team "wins the tournament".

You are given the final score of each team^† $A_1,A_2,\dots,A_N$ at the end of the tournament, and the tournament-winning team (the winner of the last match) $M$.
Determine whether there exists a progression of the tournament consistent with this information.
If one exists, output the lexicographically smallest^‡ among the winner sequences representing such a progression of the tournament.

^† The final score refers to the score after the points of the match that decides the tournament winner have been added.
^‡ For $2$ sequences $P,Q$, let $j$ be the first position where they differ; if $P_j<Q_j$, then $P$ is said to be lexicographically smaller than $Q$. However, if one is a prefix of the other, the shorter one is said to be lexicographically smaller.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $1 \leq K \leq 2\times 10^5$
• $1 \leq M \leq N$
• $0 \leq A_i \leq 2\times 10^5$
• All input values are integers

Input

The input is given from standard input in the following format.

$N\ K$
$M$
$A_1\ A_2\ \dots\ A_N$

Output

If no progression of the tournament satisfying the conditions exists, output -1 on $1$ line.

If one exists, output in the following format.

$T$
$b_1\ b_2\ \dots\ b_T$

Here, $T$ is the number of matches and $b_t$ is the team number of the winner of the $t$-th match; $T$ is an integer greater than or equal to $1$, and each $b_t$ is an integer satisfying $1 \leq b_t \leq N$.
If there are multiple winner sequences satisfying the conditions, output the lexicographically smallest one among them.

Sample

3 2
1
4 4 4

3
2 3 1

3 2
1
4 3 5

-1

4 4
1
7 6 6 6

5
1 2 3 4 1