J. Fresh Days and Lovely Days
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

I keep recalling the days in the past over and over again, afraid that if I am even a little careless, those vivid moments will quietly slip away.

Fresh days are like newly peeled orange segments, falling onto the tip of your tongue; the sour and sweet juice spreads between your teeth, and even your breath carries a refreshing fruity scent. Sunshine also falls into your palm, soft and warm like a ball of fluff, slowly rolling away between your fingers. When you try to grasp it tightly, it has already slipped away, turning into faint glimmers among the dust.

Lovely days are like a soft warm breeze soaking into the afternoon, leaving a light trace of warmth on your collar. It brushes past that gentle silhouette, circling around, stirring a soft rustle in the flowers and leaves, then slows down again, only willing to drift slowly along the hem of your clothes. The patches of light around you quietly blur into a soft halo, and the air ripples with tenderness.

How could I bear to tuck all of these away into a drawer of the past, letting their vividness slowly fade into old shadows? I know that time must move forward, yet I still cannot help wishing it would slow down a little, then a little more, so that I can look once again at the shape of every single day.

Little L recalled $$$n$$$ days and used an uppercase English letter to describe each day.

He writes them down in order and obtains a string $$$S_1S_2\cdots S_n$$$ (each $$$S_i$$$ is an uppercase English letter).

We say that the $$$i$$$-th day is a fresh day if and only if exactly one of $$$S_i\ne S_{i-1}$$$ and $$$S_i\ne S_{i+1}$$$ holds.

We say that the $$$i$$$-th day is a lovely day if and only if neither of $$$S_i\ne S_{i-1}$$$ and $$$S_i\ne S_{i+1}$$$ holds.

It is important to note that we assume that $$$\boldsymbol{S_1\ne S_0}$$$ and $$$\boldsymbol{S_n\ne S_{n+1}}$$$ here.

Little L counted and found that there are $$$m_1$$$ fresh days and $$$m_2$$$ lovely days.

As time passed, Little L forgot the string $$$S_1S_2\cdots S_n$$$, and only vaguely remembers $$$n,m_1,m_2$$$.

Given $$$n,m_1,m_2$$$, determine whether Little L could have remembered them correctly or must have remembered them incorrectly.

If Little L could have remembered them correctly, output any possible string $$$S_1S_2\cdots S_n$$$.

Input

The first line contains a single integer $$$T$$$ ($$$T\ge1$$$), denoting the number of test cases.

Then, for each test case, there is a single line containing three integers $$$n,m_1,m_2$$$ ($$$n\ge1$$$, $$$m_1,m_2\ge0$$$, $$$m_1+m_2\le n$$$).

It is guaranteed that the sum of $$$n$$$ over all $$$T$$$ test cases does not exceed $$$10^6$$$.

Output

For each test case, output one or two lines.

On the first line, output Possible or Impossible, meaning that Little L could have remembered correctly or must have remembered incorrectly, respectively.

If Little L could have remembered correctly, then on the second line output a string $$$S_1S_2\cdots S_n$$$ of length $$$n$$$ consisting of uppercase English letters.

In this case, you must ensure that the string satisfies the conditions in the statement. If there are multiple valid answers, you may output any of them.

If Little L must have remembered incorrectly, then for this test case you should output only one line.

Examples
Input
1
10 6 3
Output
Possible
ABBCCCDDDD
Input
8
1 0 0
5 2 3
6 0 0
6 4 1
8 6 2
4 2 0
1 1 0
4 0 3
Output
Possible
A
Possible
AAAAA
Possible
ABABAB
Possible
AABBBA
Possible
AABBBBAA
Possible
YXXY
Impossible
Impossible
Note

To explain the output in the first example, we highlight fresh days in blue and lovely days in green: $$$$$$ \texttt{A}\texttt{ }\color{blue}{\texttt{B}}\texttt{ }\color{blue}{\texttt{B}}\texttt{ }\color{blue}{\texttt{C}}\texttt{ }\color{green}{\texttt{C}}\texttt{ }\color{blue}{\texttt{C}}\texttt{ }\color{blue}{\texttt{D}}\texttt{ }\color{green}{\texttt{D}}\texttt{ }\color{green}{\texttt{D}}\texttt{ }\color{blue}{\texttt{D}} $$$$$$