Note

If the judge turns out to be unstable in any way, we will deal with it.

Problem Statement

Overview

Let $M$ be the maximum card value and $N$ be the number of cards in each player's hand.
For each value $v$ ($1 \leq v \leq M$), there are $v$ cards of that value, for a total of $\frac{M(M+1)}{2}$ cards.
From these, $3N$ cards are chosen and dealt to three players A, B, and C, with $N$ cards each (some cards may go unused).

A and B form a cooperative team (communication problem: the same program runs as 2 processes).
C is operated by the judge and does not ask questions.

A and B know only their own hands. Ask the game master about values and determine C's hand.

Rules

• A card of value $v$ exists in exactly $v$ copies overall
• $3N$ cards are chosen and dealt to A, B, and C, with $N$ cards each (the rest are unused)
• Turns alternate in the order A → B → A → B → ...
• On your turn, output either ASK X (a question) or GUESS c1 ... cN (an answer)
• ASK X: the game master notifies everyone that "there are $K$ cards of value $X$ in total among the three players' hands"
• GUESS: answer C's hand. If both A and B are correct, the verdict is AC

Judging

The score for one case is $ 3M - Q$ ($Q$ = the number of questions). The fewer the questions, the higher the score.

There are 16 test cases.

All input and output values are integers.

• Both players' GUESSes are correct → AC (score=$Q$)
• Even one of them is incorrect → WA
• A value violating the conditions is output → WA
• The number of questions exceeds $3M$ → QLE

Input

Initialization

You receive the following from the judge:

$id$ $N$ $M$
$c_1$ $c_2$ ... $c_N$

• $id$: player number ($1$=A, $2$=B)
• $N$: the number of cards in hand, $M$: the maximum card value
• $c_i$: your own hand (sorted in ascending order)

Each Turn

Your turn: receive TURN → output ASK X or GUESS c1 c2 ... cN

The other player's turn: receive WAIT (no output needed; wait for the result)

Question result: COUNT X K is sent to both players

Answer result: GUESSED id ok is sent to both players ($ok$: 1=correct, 0=incorrect)

End: after both players have made a GUESS, you receive END Q ($Q$=the number of questions)

Constraints

• All input and output values are integers
• $id \in \{1, 2\}$
• $2 \leq N \leq 18$
• $4 \leq M \leq 11$
• $1 \leq c_i \leq M$
• $3N \leq \frac{M(M+1)}{2}$
• ASK X must satisfy $1 \leq X \leq M$
• GUESS must output exactly $N$ integers (each from $1$ to $M$) in ascending sorted order
• Maximum number of questions: $3M$

Output

Perform input and output interactively according to the protocol.

Make sure to flush after each output.

Sample