A14609 | Red-Black Number

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.

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.

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.