Red-Black Number

题意翻译

给一个长度为 $n$ 的字符串，和整数 $A,B$。将每个位置上的字符染成红色或黑色，要求红色位置组成的十进制数是 $A$ 的倍数，黑色的是 $B$ 的倍数，求红色位置数目与黑色位置数目差的最小值。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

4
5 3 13
02165
4 2 1
1357
8 1 1
12345678
2 7 9
90

输出样例 #1

RBRBR
-1
BBRRRRBB
BR

说明

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.