A13058 | 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.

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.

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".