Chips

题意翻译

### 题目描述 有$n$个棋子排成环状,标号为$1..n$ 一开始每个棋子都是黑色或白色的。随后有$k$次操作。操作时,棋子变换的规则如下:我们考虑一个棋子本身以及与其相邻的两个棋子(共3个),如果其中白子占多数,那么这个棋子就变成白子,否则这个棋子就变成黑子。注意,对于每个棋子,在确定要变成什么颜色之后,并不会立即改变颜色,而是等到所有棋子确定变成什么颜色后,所有棋子才同时变换颜色。 对于一个棋子$i$,与其相邻的棋子是$i-1$和$i+1$。特别地,对于棋子$1$,与其相邻的棋子是$2$和$n$;对于棋子$n$,与其相邻的棋子是$1$和$n-1$。 如图是在$n=6$时进行的一次操作。 ![图像](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1244F/954a54cba9c62be21723582b0f9fdfba14d8bb72.png) 给你$n$和初始时每个棋子的颜色,你需要求出在$k$次操作后每个棋子的颜色。 ### 输入格式 第一行两个整数$n\ (3 \leq n \leq 2\cdot 10^5)$和$k\ (1 \leq k \leq 10^9)$,表示棋子总数与操作次数。 第二行是一个长度为$n$的,仅由字符$B$和$W$构成的字符串。如果第$i$个字符是$B$,表示第$i$个棋子位黑色,否则为白色。 ### 输出格式 一行,长度为$n$的,仅由字符$B$和$W$构成的字符串,描述操作完成后每个棋子的颜色。 注意输出的顺序要和输入数据中的对应。 ### 样例解释 1. 就是题目描述中举的那个例子 2. "WBWBWBW" $\rightarrow$ "WWBWBWW" $\rightarrow$ "WWWBWWW" $\rightarrow$ "WWWWWWW" 3. "BWBWBW" $\rightarrow$ "WBWBWB" $\rightarrow$ "BWBWBW" $\rightarrow$ "WBWBWB" $\rightarrow$ "BWBWBW"

题目描述

There are $ n $ chips arranged in a circle, numbered from $ 1 $ to $ n $ . Initially each chip has black or white color. Then $ k $ iterations occur. During each iteration the chips change their colors according to the following rules. For each chip $ i $ , three chips are considered: chip $ i $ itself and two its neighbours. If the number of white chips among these three is greater than the number of black chips among these three chips, then the chip $ i $ becomes white. Otherwise, the chip $ i $ becomes black. Note that for each $ i $ from $ 2 $ to $ (n - 1) $ two neighbouring chips have numbers $ (i - 1) $ and $ (i + 1) $ . The neighbours for the chip $ i = 1 $ are $ n $ and $ 2 $ . The neighbours of $ i = n $ are $ (n - 1) $ and $ 1 $ . The following picture describes one iteration with $ n = 6 $ . The chips $ 1 $ , $ 3 $ and $ 4 $ are initially black, and the chips $ 2 $ , $ 5 $ and $ 6 $ are white. After the iteration $ 2 $ , $ 3 $ and $ 4 $ become black, and $ 1 $ , $ 5 $ and $ 6 $ become white. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1244F/954a54cba9c62be21723582b0f9fdfba14d8bb72.png)Your task is to determine the color of each chip after $ k $ iterations.

输入输出格式

输入格式


The first line contains two integers $ n $ and $ k $ $ (3 \le n \le 200\,000, 1 \le k \le 10^{9}) $ — the number of chips and the number of iterations, respectively. The second line contains a string consisting of $ n $ characters "W" and "B". If the $ i $ -th character is "W", then the $ i $ -th chip is white initially. If the $ i $ -th character is "B", then the $ i $ -th chip is black initially.

输出格式


Print a string consisting of $ n $ characters "W" and "B". If after $ k $ iterations the $ i $ -th chip is white, then the $ i $ -th character should be "W". Otherwise the $ i $ -th character should be "B".

输入输出样例

输入样例 #1

6 1
BWBBWW

输出样例 #1

WBBBWW

输入样例 #2

7 3
WBWBWBW

输出样例 #2

WWWWWWW

输入样例 #3

6 4
BWBWBW

输出样例 #3

BWBWBW

说明

The first example is described in the statement. The second example: "WBWBWBW" $ \rightarrow $ "WWBWBWW" $ \rightarrow $ "WWWBWWW" $ \rightarrow $ "WWWWWWW". So all chips become white. The third example: "BWBWBW" $ \rightarrow $ "WBWBWB" $ \rightarrow $ "BWBWBW" $ \rightarrow $ "WBWBWB" $ \rightarrow $ "BWBWBW".