F. Chipstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputPrint 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".ExamplesInput
6 1
BWBBWW
Output
WBBBWW
Input
7 3
WBWBWBW
Output
WWWWWWW
Input
6 4
BWBWBW
Output
BWBWBW
NoteThe 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".
6 1
BWBBWW

WBBBWW 
['constructive algorithms', 'implementation', '*2300']