# 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".