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 main() {
  int n, k;
  cin >> n >> k;
  string str;
  cin >> str;
  if (k >= 3) {
    int ans = 0;
    for (int i = 1; i < n; i++) {
      if (str[i] == str[i - 1]) {
        ans++;
        for (int j = 0; j < 26; j++) {
          if (j + 'A' != str[i - 1]) {
            if (i != n - 1) {
              if (j + 'A' != str[i + 1]) {
                str[i] = j + 'A';
                break;
              }
            } else {
              str[i] = j + 'A';
              break;
            }
          }
        }
      }
    }
    cout << ans << "\n" << str << "\n";
  } else {
    string s;
    int ans = -1;
    for (int i = 0; i < 2; i++) {
      int k = i;
      string temp;
      for (int j = 0; j < n; j++) {
        temp.push_back('A' + k);
        k = !k;
      }
      int count = 0;
      for (int j = 0; j < n; j++) {
        if (temp[j] != str[j]) count++;
      }
      if (ans == -1 || ans > count) {
        ans = count;
        s = temp;
      }
    }
    cout << ans << "\n" << s << "\n";
  }
  return 0;
}