#include <bits/stdc++.h>
using namespace std;
int n, k;
char s[200100];
int pa[200100];
int rank1[200100];
int find(int x) {
  if (pa[x] == x)
    return x;
  else {
    return pa[x] = find(pa[x]);
  }
}
void unite(int x, int y) {
  int px = find(x);
  int py = find(y);
  if (px != py) {
    if (rank1[px] < rank1[py]) {
      pa[px] = py;
    } else {
      pa[py] = px;
      if (rank1[px] == rank1[py]) {
        rank1[px]++;
      }
    }
  }
}
int left(int x) {
  if (x == 1)
    return n;
  else
    return (x - 1);
}
int right(int x) {
  if (x == n)
    return 1;
  else
    return (x + 1);
}
int r[200100];
int l[200100];
int main() {
  scanf("%d%d", &n, &k);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i++) {
    pa[i] = i;
    rank1[i] = 1;
  }
  for (int i = 1; i <= n; i++) {
    if (i == 1) {
      if (s[n] == s[1]) {
        unite(1, n);
      }
      if (s[1] == s[2]) {
        unite(1, 2);
      }
    } else if (i == n) {
      if (s[n] == s[1]) {
        unite(1, n);
      }
      if (s[n] == s[n - 1]) {
        unite(n, n - 1);
      }
    } else {
      if (s[i] == s[i - 1]) {
        unite(i, i - 1);
      }
      if (s[i] == s[i + 1]) unite(i, i + 1);
    }
  }
  int temp = 0;
  for (int i = 1; i <= n; i++) {
    if (rank1[i] != 1 && find(i) == i) {
      temp = i;
      break;
    }
  }
  if (temp == 0) {
    if (k % 2 == 0)
      printf("%s", s + 1);
    else {
      for (int i = 1; i <= n; i++) {
        if (s[i] == 'W')
          printf("B");
        else
          printf("W");
      }
    }
  } else {
    int cnt = 0;
    int temp1 = right(temp);
    while (temp1 != temp) {
      if (find(temp1) == temp1 && rank1[temp1] == 1) {
        if (l[cnt] == 0) {
          l[cnt] = temp1;
        }
      } else {
        if (l[cnt] != 0 && r[cnt] == 0) {
          int temp2 = left(temp1);
          r[cnt++] = temp2;
        }
      }
      temp1 = right(temp1);
    }
    if (l[cnt] != 0 && r[cnt] == 0) {
      int temp2 = left(temp1);
      r[cnt++] = temp2;
    }
    for (int i = 0; i < cnt; i++) {
      if (r[i] == l[i]) {
        if (s[left(r[i])] == s[right(r[i])]) {
          s[r[i]] = s[left(r[i])];
        }
      } else {
        int cnt1 = 1;
        for (int j1 = l[i], j2 = r[i];;) {
          if (left(j1) == j2) break;
          if (j1 == j2 && cnt1 <= k) {
            if (s[left(j1)] == s[right(j1)]) {
              s[j1] = s[left(j1)];
            }
            break;
          } else if (j1 == j2 && cnt1 > k) {
            if (k % 2 == 1) {
              if (s[j1] == 'W')
                s[j1] = 'B';
              else
                s[j1] = 'W';
            }
            break;
          } else {
            if (cnt1 <= k) {
              char s1 = s[left(l[i])];
              char s2 = s[right(r[i])];
              s[j1] = s1;
              s[j2] = s2;
            } else {
              if (k % 2 == 1) {
                if (s[j1] == 'W')
                  s[j1] = 'B';
                else
                  s[j1] = 'W';
                if (s[j2] == 'W')
                  s[j2] = 'B';
                else
                  s[j2] = 'W';
              }
            }
          }
          j1 = right(j1);
          j2 = left(j2);
          cnt1++;
        }
      }
    }
    printf("%s", s + 1);
  }
  return 0;
}

### 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;
int n, k;
char s[200100];
int pa[200100];
int rank1[200100];
int find(int x) {
  if (pa[x] == x)
    return x;
  else {
    return pa[x] = find(pa[x]);
  }
}
void unite(int x, int y) {
  int px = find(x);
  int py = find(y);
  if (px != py) {
    if (rank1[px] < rank1[py]) {
      pa[px] = py;
    } else {
      pa[py] = px;
      if (rank1[px] == rank1[py]) {
        rank1[px]++;
      }
    }
  }
}
int left(int x) {
  if (x == 1)
    return n;
  else
    return (x - 1);
}
int right(int x) {
  if (x == n)
    return 1;
  else
    return (x + 1);
}
int r[200100];
int l[200100];
int main() {
  scanf("%d%d", &n, &k);
  scanf("%s", s + 1);
  for (int i = 1; i <= n; i++) {
    pa[i] = i;
    rank1[i] = 1;
  }
  for (int i = 1; i <= n; i++) {
    if (i == 1) {
      if (s[n] == s[1]) {
        unite(1, n);
      }
      if (s[1] == s[2]) {
        unite(1, 2);
      }
    } else if (i == n) {
      if (s[n] == s[1]) {
        unite(1, n);
      }
      if (s[n] == s[n - 1]) {
        unite(n, n - 1);
      }
    } else {
      if (s[i] == s[i - 1]) {
        unite(i, i - 1);
      }
      if (s[i] == s[i + 1]) unite(i, i + 1);
    }
  }
  int temp = 0;
  for (int i = 1; i <= n; i++) {
    if (rank1[i] != 1 && find(i) == i) {
      temp = i;
      break;
    }
  }
  if (temp == 0) {
    if (k % 2 == 0)
      printf("%s", s + 1);
    else {
      for (int i = 1; i <= n; i++) {
        if (s[i] == 'W')
          printf("B");
        else
          printf("W");
      }
    }
  } else {
    int cnt = 0;
    int temp1 = right(temp);
    while (temp1 != temp) {
      if (find(temp1) == temp1 && rank1[temp1] == 1) {
        if (l[cnt] == 0) {
          l[cnt] = temp1;
        }
      } else {
        if (l[cnt] != 0 && r[cnt] == 0) {
          int temp2 = left(temp1);
          r[cnt++] = temp2;
        }
      }
      temp1 = right(temp1);
    }
    if (l[cnt] != 0 && r[cnt] == 0) {
      int temp2 = left(temp1);
      r[cnt++] = temp2;
    }
    for (int i = 0; i < cnt; i++) {
      if (r[i] == l[i]) {
        if (s[left(r[i])] == s[right(r[i])]) {
          s[r[i]] = s[left(r[i])];
        }
      } else {
        int cnt1 = 1;
        for (int j1 = l[i], j2 = r[i];;) {
          if (left(j1) == j2) break;
          if (j1 == j2 && cnt1 <= k) {
            if (s[left(j1)] == s[right(j1)]) {
              s[j1] = s[left(j1)];
            }
            break;
          } else if (j1 == j2 && cnt1 > k) {
            if (k % 2 == 1) {
              if (s[j1] == 'W')
                s[j1] = 'B';
              else
                s[j1] = 'W';
            }
            break;
          } else {
            if (cnt1 <= k) {
              char s1 = s[left(l[i])];
              char s2 = s[right(r[i])];
              s[j1] = s1;
              s[j2] = s2;
            } else {
              if (k % 2 == 1) {
                if (s[j1] == 'W')
                  s[j1] = 'B';
                else
                  s[j1] = 'W';
                if (s[j2] == 'W')
                  s[j2] = 'B';
                else
                  s[j2] = 'W';
              }
            }
          }
          j1 = right(j1);
          j2 = left(j2);
          cnt1++;
        }
      }
    }
    printf("%s", s + 1);
  }
  return 0;
}

```