Red-Black Number solution codeforces

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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.

$\text{[math]}$ Example of painting a number for

A = 3

and

B = 13

The figure above shows an example of painting the number

x = 02165

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.

Red-Black Number solution codeforces

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

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

Red-Black Number solution codeforces

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.

Red-Black Number solution codeforces

input

Copy

Red-Black Number solution codeforces

Copy

RBRBR
-1
BBRRRRBB
BR

Red-Black Number solution codeforces

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.

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Red-Black Number solution codeforces

For Solution

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Red-Black Number solution codeforces

Red-Black Number solution codeforces

Red-Black Number solution codeforces

Red-Black Number solution codeforces

Red-Black Number solution codeforces

For Solution

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