#include <bits/stdc++.h>
using namespace std;
const long long MAXN = 200001;
long long n, k;
long long arr[MAXN];
long long dist[MAXN];
long long lc[MAXN];
long long rc[MAXN];
vector<pair<long long, long long> > ranges;
signed main() {
  ios::sync_with_stdio(false);
  cin >> n >> k;
  for (long long i = 0; i < n; i++) {
    char c;
    cin >> c;
    if (c == 'B') arr[i] = 1;
  }
  bool flag1 = (n % 2 == 0);
  if (flag1)
    for (long long i = 0; i < n; i++) {
      if (arr[0] ^ arr[i] ^ (i & 1)) {
        flag1 = false;
        break;
      }
    }
  if (flag1) {
    cerr << "I AK IOI" << endl;
    for (long long i = 0; i < n; i++) {
      if (arr[i] ^ (k & 1))
        cout << 'B';
      else
        cout << 'W';
    }
    cout << endl;
    exit(0);
  }
  long long bg = 0;
  for (long long i = 0; i < n; i++) {
    if (i != 0 && arr[i - 1] == arr[i]) {
      bg = i;
      break;
    }
  }
  bg += n;
  long long lastpos = 0;
  long long lastcol = 0;
  for (long long i = bg; i < bg + n; i++) {
    if (arr[(i - 1) % n] != arr[i % n] && arr[i % n] != arr[(i + 1) % n]) {
      dist[i % n] = i - lastpos;
      lc[i % n] = lastcol;
    } else {
      lastpos = i;
      lastcol = arr[i % n];
      dist[i % n] = 0;
    }
  }
  bg += n;
  for (long long i = bg - 1; i >= bg - n; i--) {
    if (arr[(i - 1) % n] != arr[i % n] && arr[i % n] != arr[(i + 1) % n]) {
      if (lastpos - i < dist[i % n]) {
        dist[i % n] = i - lastpos;
      }
      rc[i % n] = lastcol;
    } else {
      lastpos = i;
      lastcol = arr[i % n];
    }
  }
  for (long long i = 0; i < n; i++) {
    if (dist[i] == 0) {
      if (arr[i])
        cout << 'B';
      else
        cout << 'W';
    } else if (dist[i] > 0) {
      if (k < dist[i]) {
        if (arr[i] ^ (k & 1))
          cout << 'B';
        else
          cout << 'W';
      } else {
        if (lc[i])
          cout << 'B';
        else
          cout << 'W';
      }
    } else {
      if (k < -dist[i]) {
        if (arr[i] ^ (k & 1))
          cout << 'B';
        else
          cout << 'W';
      } else {
        if (rc[i])
          cout << 'B';
        else
          cout << 'W';
      }
    }
  }
  cout << endl;
}

### Prompt

Your task is to create a CPP solution to 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 long long MAXN = 200001;
long long n, k;
long long arr[MAXN];
long long dist[MAXN];
long long lc[MAXN];
long long rc[MAXN];
vector<pair<long long, long long> > ranges;
signed main() {
  ios::sync_with_stdio(false);
  cin >> n >> k;
  for (long long i = 0; i < n; i++) {
    char c;
    cin >> c;
    if (c == 'B') arr[i] = 1;
  }
  bool flag1 = (n % 2 == 0);
  if (flag1)
    for (long long i = 0; i < n; i++) {
      if (arr[0] ^ arr[i] ^ (i & 1)) {
        flag1 = false;
        break;
      }
    }
  if (flag1) {
    cerr << "I AK IOI" << endl;
    for (long long i = 0; i < n; i++) {
      if (arr[i] ^ (k & 1))
        cout << 'B';
      else
        cout << 'W';
    }
    cout << endl;
    exit(0);
  }
  long long bg = 0;
  for (long long i = 0; i < n; i++) {
    if (i != 0 && arr[i - 1] == arr[i]) {
      bg = i;
      break;
    }
  }
  bg += n;
  long long lastpos = 0;
  long long lastcol = 0;
  for (long long i = bg; i < bg + n; i++) {
    if (arr[(i - 1) % n] != arr[i % n] && arr[i % n] != arr[(i + 1) % n]) {
      dist[i % n] = i - lastpos;
      lc[i % n] = lastcol;
    } else {
      lastpos = i;
      lastcol = arr[i % n];
      dist[i % n] = 0;
    }
  }
  bg += n;
  for (long long i = bg - 1; i >= bg - n; i--) {
    if (arr[(i - 1) % n] != arr[i % n] && arr[i % n] != arr[(i + 1) % n]) {
      if (lastpos - i < dist[i % n]) {
        dist[i % n] = i - lastpos;
      }
      rc[i % n] = lastcol;
    } else {
      lastpos = i;
      lastcol = arr[i % n];
    }
  }
  for (long long i = 0; i < n; i++) {
    if (dist[i] == 0) {
      if (arr[i])
        cout << 'B';
      else
        cout << 'W';
    } else if (dist[i] > 0) {
      if (k < dist[i]) {
        if (arr[i] ^ (k & 1))
          cout << 'B';
        else
          cout << 'W';
      } else {
        if (lc[i])
          cout << 'B';
        else
          cout << 'W';
      }
    } else {
      if (k < -dist[i]) {
        if (arr[i] ^ (k & 1))
          cout << 'B';
        else
          cout << 'W';
      } else {
        if (rc[i])
          cout << 'B';
        else
          cout << 'W';
      }
    }
  }
  cout << endl;
}

```