**This is an interactive problem.**
There are $\tbinom{2N}{N}$ cards numbered $1$ to $\tbinom{2N}{N}$ on a desk. Card $i$ $(1 \le i \le \tbinom{2N}{N})$ shows on its front the $i$‑th string in lexicographic order among the strings consisting of $N$ zeros and $N$ ones.
Example For $N = 2$, the fronts of cards $1$, $2$, $3$, $4$, $5$, $6$ are `0011`, `0101`, `0110`, `1001`, `1010`, `1100`, respectively.
Witch Alice writes one of the first $N$ uppercase letters (for example, `A` or `B` if $N = 2$) on the back of each card, then performs the following **magic** $T$ times.
> **A single magic**
>
> 1. The host announces a letter $s$ among the first $N$ uppercase letters.
> 2. The host writes a length-$2N$ string of all `0` on the blackboard.
> 3. For $i = 1, 2, \dots, N$ in this order, do the following. Here, $a_1, b_1, \dots, a_N, b_N$ are distinct integers from $1$ to $2N$.
> * First, the host tells Alice integers $a_i$ and $b_i$.
> * Then, Alice chooses exactly one of the $a_i$\-th and $b_i$\-th characters of the string on the blackboard, and sets it to `1`.
> 4. Let $x$ be the final string on the blackboard. Exactly one card shows $x$ on its front; look at its back. The magic succeeds if and only if the letter on its back equals $s$.
Note that Alice learns $a_{i+1}$ and $b_{i+1}$ only after choosing which of the $a_i$\-th and $b_i$\-th characters to set to `1`.
Implement a strategy that makes all $T$ magics succeed. Now, let us begin.
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## Constraints
* $2 \le N \le 10$
* $1 \le T \le 5\,000$
* The letter $s$ is among the first $N$ uppercase letters.
* $1 \le a_i < b_i \le 2N$
* $a_1, b_1, a_2, b_2, \dots, a_N, b_N$ are distinct.
* $a_1, b_1, a_2, b_2, \dots, a_N, b_N, s$ are fixed before the interaction starts.
* $N, T, a_i, b_i$ are integers.
## Input And Output
First, read the integers $N$ and $T$ given from Standard Input in the following format:
$N$ $T$
Next, let $c_i$ be the letter written on the back of card $i$, and print those letters in the following format, followed by a newline. Here, $c_i$ must be among the first $N$ uppercase letters.
$c_1 c_2 \cdots c_{\tbinom{2N}{N}}$
Next, repeat the following process $T$ times. The $t$\-th iteration $(1 \leq t \leq T)$ corresponds to the $t$\-th magic.
> Read the announced letter $s$ given in the following format:
>
> $s$
>
> Then, for $i = 1, 2, \dots, N$ in this order, do the following.
>
> * Read integers $a_i$ and $b_i$ given in the following format:
>
> $a_i$ $b_i$
>
> * Print the chosen position $d$ in the following format, followed by a newline. Here, $d$ must be $a_i$ or $b_i$.
>
> $d$
>
> If your output was malformed or the previous magic failed, no more input such as $s$ or $(a_i, b_i)$ is given, but `-1` is given from Standard Input. In this case, exit immediately. (If you fail for the first time in the $T$\-th magic, or your output was malformed for the first time at $i = N$ in the $T$\-th magic, no more input follows.)
[samples]
## Notes
**Flush after every output.** Otherwise, you may receive a TLE verdict.
If you read `-1`, exit immediately. If you do so, you will receive a WA verdict, but continuing leads to an indeterminate verdict. Unnecessary newlines may be seen as malformed.
The judge is **non‑adaptive**; the values $a_1, b_1, a_2, b_2, \dots, a_N, b_N, s$ are fixed before the interaction starts, and will not be affected by your output.
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