CF1244F.Chips

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.

Your task is to determine the color of each chip after $k$ iterations.

有 $n$ 个芯片围成一个圆圈，编号为 $1$ 到 $n$。

初始时，每个芯片为黑色或白色。随后进行 $k$ 轮迭代。在每轮迭代中，所有芯片根据以下规则同时更新其颜色：对每个芯片 $i$，考察三个芯片——芯片 $i$ 自身及其两个相邻芯片。若这三个芯片中白色芯片的数量大于黑色芯片的数量，则芯片 $i$ 变为白色；否则，芯片 $i$ 变为黑色。

注意：对每个 $i$（$2 \le i \le n-1$），其两个相邻芯片的编号分别为 $(i-1)$ 和 $(i+1)$；芯片 $i = 1$ 的相邻芯片为 $n$ 和 $2$；芯片 $i = n$ 的相邻芯片为 $(n-1)$ 和 $1$。

下图描述了 $n = 6$ 时的一轮迭代过程：初始时，芯片 $1$、$3$、$4$ 为黑色，芯片 $2$、$5$、$6$ 为白色；经过该轮迭代后，芯片 $2$、$3$、$4$ 变为黑色，芯片 $1$、$5$、$6$ 变为白色。

你的任务是确定经过 $k$ 轮迭代后每个芯片的颜色。

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.

第一行包含两个整数 $n$ 和 $k$（$3 \le n \le 200\,000$，$1 \le k \le 10^{9}$），分别表示芯片的数量和迭代次数。

第二行包含一个由 $n$ 个字符 "W" 和 "B" 组成的字符串。若第 $i$ 个字符为 "W"，则第 $i$ 个芯片初始为白色；若第 $i$ 个字符为 "B"，则第 $i$ 个芯片初始为黑色。

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".

输出一个由 $n$ 个字符 "W" 和 "B" 组成的字符串。如果经过 $k$ 次迭代后，第 $i$ 个芯片为白色，则该字符串的第 $i$ 个字符应为 "W"；否则应为 "B"。

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".

第一个示例在题目描述中已给出。

第二个示例："WBWBWBW" $\rightarrow$ "WWBWBWW" $\rightarrow$ "WWWBWWW" $\rightarrow$ "WWWWWWW"。因此所有棋子均变为白色。

第三个示例："BWBWBW" $\rightarrow$ "WBWBWB" $\rightarrow$ "BWBWBW" $\rightarrow$ "WBWBWB" $\rightarrow$ "BWBWBW"。