Problem: A colored stripe is represented by a horizontal row of n square cells, each cell is pained one of k colors. Your task is to repaint the minimum number of cells so that no two neighbouring cells are of the same color. You can use any color from 1 to k to repaint the cells.

Input

The first input line contains two integers n and k (1 ≤ n ≤ 5·105; 2 ≤ k ≤ 26). The second line contains n uppercase English letters. Letter "A" stands for the first color, letter "B" stands for the second color and so on. The first k English letters may be used. Each letter represents the color of the corresponding cell of the stripe.

Output

Print a single integer — the required minimum number of repaintings. In the second line print any possible variant of the repainted stripe.

Examples

Input

6 3
ABBACC


Output

2
ABCACA


Input

3 2
BBB


Output

1
BAB

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, k;
char ffpc(char a, char b) {
  for (int i = 0; i < k; ++i) {
    char c = i + 'A';
    if (c != a && c != b) return char(c);
  }
}
int main() {
  cin >> n >> k;
  string s;
  cin >> s;
  if (k == 2) {
    int cnt = 0;
    for (int i = 0; i < n; ++i)
      if (i % 2 == 0 && s[i] != 'A')
        ++cnt;
      else if (i % 2 && s[i] != 'B')
        ++cnt;
    if (cnt <= n - cnt) {
      cout << cnt << endl;
      for (int i = 0; i < n; ++i)
        if (i % 2 == 0)
          cout << 'A';
        else
          cout << 'B';
    } else {
      cout << n - cnt << endl;
      for (int i = 0; i < n; ++i)
        if (i % 2 == 0)
          cout << 'B';
        else
          cout << 'A';
    }
    return 0;
  }
  int last = 0, cnt = 0;
  s += '!';
  string str = "";
  for (int i = 1; i <= n; ++i)
    if (s[i] != s[last]) {
      str += s[last];
      for (int j = 1; j < i - last - 1; ++j)
        if (j % 2) {
          str += ffpc(s[last], '#');
          ++cnt;
        } else
          str += s[last];
      if (i - last - 1 > 0) {
        if ((i - last - 1) % 2) {
          str += ffpc(s[last], s[i]);
          ++cnt;
        } else
          str += s[last];
      }
      last = i;
    }
  cout << cnt << endl << str;
}