#include <bits/stdc++.h>
#pragma GCC optimize(2)
using namespace std;
const int maxn = 2e5;
const int INF = 0x7fffffff;
const int mod = 1e9 + 7;
const double eps = 1e-7;
const double Pi = acos(-1.0);
inline int read_int() {
  char c;
  int ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long read_ll() {
  char c;
  long long ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long quick_pow(long long base, long long index, long long p) {
  long long res = 1;
  while (index) {
    if (index & 1) res = res * base % p;
    base = base * base % p;
    index >>= 1;
  }
  return res;
}
int n, k;
int dist[maxn + 5];
int prev(int x) { return x == 0 ? n - 1 : x - 1; }
int next(int x) { return x == n - 1 ? 0 : x + 1; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  vector<int> a(n);
  string s;
  cin >> s;
  for (int i = 0; i < n; i++) {
    a[i] = s[i] == 'W';
  }
  memset(dist, -1, sizeof dist);
  queue<int> q;
  for (int i = 0; i < n; i++) {
    if (i == 0) {
      if (a[n - 1] == a[i] || a[i + 1] == a[i]) dist[i] = 0;
    } else if (i == n - 1) {
      if (a[i - 1] == a[i] || a[0] == a[i]) dist[i] = 0;
    } else {
      if (a[i - 1] == a[i] || a[i + 1] == a[i]) dist[i] = 0;
    }
    if (dist[i] == 0) {
      q.push(i);
    }
  }
  if (q.empty()) {
    for (int i = 0; i < n; i++) {
      if (k & 1) {
        cout << (s[i] == 'W' ? 'B' : 'W');
      } else {
        cout << s[i];
      }
    }
    cout << '\n';
    return 0;
  }
  while (!q.empty()) {
    int f = q.front();
    q.pop();
    if (dist[prev(f)] == -1) {
      dist[prev(f)] = dist[f] + 1;
      q.push(prev(f));
    }
    if (dist[next(f)] == -1) {
      dist[next(f)] = dist[f] + 1;
      q.push(next(f));
    }
  }
  for (int i = 0; i < n; i++) {
    int K = min(k, dist[i]);
    if (K & 1) {
      cout << (s[i] == 'W' ? 'B' : 'W');
    } else {
      cout << s[i];
    }
  }
  cout << '\n';
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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>
#pragma GCC optimize(2)
using namespace std;
const int maxn = 2e5;
const int INF = 0x7fffffff;
const int mod = 1e9 + 7;
const double eps = 1e-7;
const double Pi = acos(-1.0);
inline int read_int() {
  char c;
  int ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long read_ll() {
  char c;
  long long ret = 0, sgn = 1;
  do {
    c = getchar();
  } while ((c < '0' || c > '9') && c != '-');
  if (c == '-')
    sgn = -1;
  else
    ret = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') ret = ret * 10 + (c - '0');
  return sgn * ret;
}
inline long long quick_pow(long long base, long long index, long long p) {
  long long res = 1;
  while (index) {
    if (index & 1) res = res * base % p;
    base = base * base % p;
    index >>= 1;
  }
  return res;
}
int n, k;
int dist[maxn + 5];
int prev(int x) { return x == 0 ? n - 1 : x - 1; }
int next(int x) { return x == n - 1 ? 0 : x + 1; }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  vector<int> a(n);
  string s;
  cin >> s;
  for (int i = 0; i < n; i++) {
    a[i] = s[i] == 'W';
  }
  memset(dist, -1, sizeof dist);
  queue<int> q;
  for (int i = 0; i < n; i++) {
    if (i == 0) {
      if (a[n - 1] == a[i] || a[i + 1] == a[i]) dist[i] = 0;
    } else if (i == n - 1) {
      if (a[i - 1] == a[i] || a[0] == a[i]) dist[i] = 0;
    } else {
      if (a[i - 1] == a[i] || a[i + 1] == a[i]) dist[i] = 0;
    }
    if (dist[i] == 0) {
      q.push(i);
    }
  }
  if (q.empty()) {
    for (int i = 0; i < n; i++) {
      if (k & 1) {
        cout << (s[i] == 'W' ? 'B' : 'W');
      } else {
        cout << s[i];
      }
    }
    cout << '\n';
    return 0;
  }
  while (!q.empty()) {
    int f = q.front();
    q.pop();
    if (dist[prev(f)] == -1) {
      dist[prev(f)] = dist[f] + 1;
      q.push(prev(f));
    }
    if (dist[next(f)] == -1) {
      dist[next(f)] = dist[f] + 1;
      q.push(next(f));
    }
  }
  for (int i = 0; i < n; i++) {
    int K = min(k, dist[i]);
    if (K & 1) {
      cout << (s[i] == 'W' ? 'B' : 'W');
    } else {
      cout << s[i];
    }
  }
  cout << '\n';
  return 0;
}

```