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;
char s[30];
void pre() {
  s[1] = 'A';
  for (int i = 2; i <= 26; i++) s[i] = (char)((int)s[i - 1] + 1);
}
int main() {
  pre();
  string str;
  int m, n, i, j, k, l, t;
  cin >> n >> k;
  cin >> str;
  int ans = 0, ans2 = 0;
  if (k == 2) {
    for (i = 0; i < n; i++) {
      if (i % 2 == 0) {
        if (str[i] != 'A') ans++;
        if (str[i] != 'B') ans2++;
        continue;
      }
      if (str[i] != 'B') ans++;
      if (str[i] != 'A') ans2++;
    }
    cout << min(ans, ans2) << "\n";
    if (ans < ans2) {
      for (i = 0; i < n; i++) {
        if (i % 2 == 0)
          cout << "A";
        else
          cout << "B";
      }
    } else {
      for (i = 0; i < n; i++) {
        if (i % 2 == 0)
          cout << "B";
        else
          cout << "A";
      }
    }
    return 0;
  }
  for (i = 0; i < n; i++) {
    j = i;
    while (str[i] == str[j]) {
      j++;
    }
    for (t = i + 1; t < j; t += 2) {
      for (l = 1; l <= k; l++) {
        if (t == j - 1 && t + 1 < n) {
          if (s[l] != str[t - 1] && s[l] != str[t + 1]) {
            str[t] = s[l];
            ans++;
            break;
          }
          continue;
        }
        if (s[l] != str[t - 1]) {
          str[t] = s[l];
          ans++;
          break;
        }
      }
    }
    i = j - 1;
  }
  cout << ans << "\n";
  cout << str;
  return 0;
}