F. Red-Black Number
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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.

Example
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.