You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
It is given a non-negative integer $$$x$$$, the decimal representation of which contains $$$n$$$ digits. You need to color each its digit in red or black, so that the number formed by the red digits is divisible by $$$A$$$, and the number formed by the black digits is divisible by $$$B$$$.

At least one digit must be colored in each of two colors. Consider, the count of digits colored in red is $$$r$$$ and the count of digits colored in black is $$$b$$$. Among all possible colorings of the given number $$$x$$$, you need to output any such that the value of $$$|r - b|$$$ is the minimum possible.

Note that the number $$$x$$$ and the numbers formed by digits of each color, may contain leading zeros.

Example of painting a number for $$$A = 3$$$ and $$$B = 13$$$

The figure above shows an example of painting the number $$$x = 02165$$$ of $$$n = 5$$$ digits for $$$A = 3$$$ and $$$B = 13$$$. The red digits form the number $$$015$$$, which is divisible by $$$3$$$, and the black ones — $$$26$$$, which is divisible by $$$13$$$. Note that the absolute value of the difference between the counts of red and black digits is $$$1$$$, it is impossible to achieve a smaller value.

## Input Format
The first line contains one integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of test cases. Then $$$t$$$ test cases follow.

Each test case consists of two lines. The first line contains three integers $$$n$$$, $$$A$$$, $$$B$$$ ($$$2 \le n \le 40$$$, $$$1 \le A, B \le 40$$$). The second line contains a non-negative integer $$$x$$$ containing exactly $$$n$$$ digits and probably containing leading zeroes.

## Output Format
For each test case, output in a separate line:

- -1 if the desired coloring does not exist;
- a string $$$s$$$ of $$$n$$$ characters, each of them is a letter 'R' or 'B'. If the $$$i$$$-th digit of the number $$$x$$$ is colored in red, then the $$$i$$$-th character of the string $$$s$$$ must be the letter 'R', otherwise the letter 'B'.

The number formed by digits colored red should divisible by $$$A$$$. The number formed by digits colored black should divisible by $$$B$$$. The value $$$|r-b|$$$ should be minimal, where $$$r$$$ is the count of red digits, $$$b$$$ is the count of black digits. If there are many possible answers, print any of them.

## Examples
```input
4
5 3 13
02165
4 2 1
1357
8 1 1
12345678
2 7 9
90
```
```output
RBRBR
-1
BBRRRRBB
BR
```

## Note
The first test case is considered in the statement.

In the second test case, there are no even digits, so it is impossible to form a number from its digits that is divisible by $$$2$$$.

In the third test case, each coloring containing at least one red and one black digit is possible, so you can color $$$4$$$ digits in red and $$$4$$$ in black ($$$|4 - 4| = 0$$$, it is impossible to improve the result).

In the fourth test case, there is a single desired coloring.

Now solve the problem and return the code.