#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
int n, k;
bool stable[N];
int stt = 0;
string s;
bool canBeStable() {
  if (s[0] == s[n - 1]) return true;
  for (int i = 1; i < n; i++)
    if (s[i] == s[i - 1]) return true;
  return false;
}
string toStable() {
  if (s[0] == s[n - 1]) return s;
  string ans = "";
  for (int i = 1; i < n; i++) {
    if (s[i] == s[i - 1]) {
      stt = i;
      break;
    }
  }
  for (int i = stt; i < n; i++) ans.push_back(s[i]);
  for (int i = 0; i < stt; i++) ans.push_back(s[i]);
  return ans;
}
void printExit(bool reverse) {
  string ans = s;
  if (stt > 0) {
    ans = "";
    for (int i = n - stt; i < n; i++) ans.push_back(s[i]);
    for (int i = 0; i < n - stt; i++) ans.push_back(s[i]);
  }
  for (int i = 0; i < n; i++) {
    if (reverse) {
      if (ans[i] == '0')
        cout << 'W';
      else
        cout << 'B';
    } else {
      if (ans[i] == '0')
        cout << 'B';
      else
        cout << 'W';
    }
  }
  exit(0);
}
void handleCycle(int st, int en) {
  if (st == -1 || en == -1) return;
  if (st == en) {
    s[st] = s[st - 1];
    return;
  }
  int copyK = k;
  bool even = ((st - en + 1) % 2 == 0 ? true : false);
  for (; st < en; st++, en--) {
    if (copyK == 0) break;
    copyK--;
    s[st] = s[st - 1];
    s[en] = s[en + 1];
  }
  if (!even && copyK > 0) {
    s[st] = s[st - 1];
    return;
  }
  if (even && copyK > 0) {
    s[st] = s[st + 1];
    s[en] = s[en - 1];
  }
  if (k % 2 == 1)
    for (int i = st; i <= en; i++) s[i] = (char)(('1' - s[i]) + '0');
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  cin >> s;
  n = s.length();
  for (int i = 0; i < n; i++) {
    if (s[i] == 'B')
      s[i] = '0';
    else
      s[i] = '1';
  }
  if (!canBeStable()) {
    k %= 2;
    if (k == 0)
      printExit(false);
    else
      printExit(true);
  }
  s = toStable();
  stable[0] = true;
  for (int i = 1; i < n; i++)
    if (s[i] == s[i - 1])
      stable[i - 1] = stable[i] = true;
    else
      stable[i] = false;
  stable[n - 1] = true;
  int st = -1, en = -1;
  for (int i = 1; i < n; i++) {
    if (!stable[i] && stable[i - 1]) st = i;
    if (st != -1 && stable[i] && !stable[i - 1]) en = i - 1;
    handleCycle(st, en);
    if (st != -1 && en != -1) st = en = -1;
  }
  printExit(false);
  return 0;
}

### Prompt

Create a solution in CPP for the following problem:

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.

<image>

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

Input

The first line contains two integers n and k (3 ≤ n ≤ 200 000, 1 ≤ k ≤ 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.

Output

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".

Examples

Input


6 1
BWBBWW


Output


WBBBWW


Input


7 3
WBWBWBW


Output


WWWWWWW


Input


6 4
BWBWBW


Output


BWBWBW

Note

The first example is described in the statement.

The second example: "WBWBWBW" → "WWBWBWW" → "WWWBWWW" → "WWWWWWW". So all chips become white.

The third example: "BWBWBW" → "WBWBWB" → "BWBWBW" → "WBWBWB" → "BWBWBW".

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
int n, k;
bool stable[N];
int stt = 0;
string s;
bool canBeStable() {
  if (s[0] == s[n - 1]) return true;
  for (int i = 1; i < n; i++)
    if (s[i] == s[i - 1]) return true;
  return false;
}
string toStable() {
  if (s[0] == s[n - 1]) return s;
  string ans = "";
  for (int i = 1; i < n; i++) {
    if (s[i] == s[i - 1]) {
      stt = i;
      break;
    }
  }
  for (int i = stt; i < n; i++) ans.push_back(s[i]);
  for (int i = 0; i < stt; i++) ans.push_back(s[i]);
  return ans;
}
void printExit(bool reverse) {
  string ans = s;
  if (stt > 0) {
    ans = "";
    for (int i = n - stt; i < n; i++) ans.push_back(s[i]);
    for (int i = 0; i < n - stt; i++) ans.push_back(s[i]);
  }
  for (int i = 0; i < n; i++) {
    if (reverse) {
      if (ans[i] == '0')
        cout << 'W';
      else
        cout << 'B';
    } else {
      if (ans[i] == '0')
        cout << 'B';
      else
        cout << 'W';
    }
  }
  exit(0);
}
void handleCycle(int st, int en) {
  if (st == -1 || en == -1) return;
  if (st == en) {
    s[st] = s[st - 1];
    return;
  }
  int copyK = k;
  bool even = ((st - en + 1) % 2 == 0 ? true : false);
  for (; st < en; st++, en--) {
    if (copyK == 0) break;
    copyK--;
    s[st] = s[st - 1];
    s[en] = s[en + 1];
  }
  if (!even && copyK > 0) {
    s[st] = s[st - 1];
    return;
  }
  if (even && copyK > 0) {
    s[st] = s[st + 1];
    s[en] = s[en - 1];
  }
  if (k % 2 == 1)
    for (int i = st; i <= en; i++) s[i] = (char)(('1' - s[i]) + '0');
  return;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  cin >> s;
  n = s.length();
  for (int i = 0; i < n; i++) {
    if (s[i] == 'B')
      s[i] = '0';
    else
      s[i] = '1';
  }
  if (!canBeStable()) {
    k %= 2;
    if (k == 0)
      printExit(false);
    else
      printExit(true);
  }
  s = toStable();
  stable[0] = true;
  for (int i = 1; i < n; i++)
    if (s[i] == s[i - 1])
      stable[i - 1] = stable[i] = true;
    else
      stable[i] = false;
  stable[n - 1] = true;
  int st = -1, en = -1;
  for (int i = 1; i < n; i++) {
    if (!stable[i] && stable[i - 1]) st = i;
    if (st != -1 && stable[i] && !stable[i - 1]) en = i - 1;
    handleCycle(st, en);
    if (st != -1 && en != -1) st = en = -1;
  }
  printExit(false);
  return 0;
}

```