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, ans = 0;
string s;
void change(int h) {
  int c1;
  if (h < n - 1) {
    c1 = s[h + 1] - 'A';
  } else {
    c1 = s[h - 1] - 'A';
  }
  int c = s[h] - 'A';
  for (int i = 0; i < k; i++) {
    if (i != c && i != c1) {
      s[h] = char('A' + i);
    }
  }
}
int main() {
  cin >> n >> k >> s;
  if (k == 2) {
    int cn1 = 0, cn2 = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] - 'A' != i % 2) {
        cn1++;
      } else {
        cn2++;
      }
    }
    if (cn1 < cn2) {
      for (int i = 0; i < n; i++) {
        if (s[i] - 'A' != i % 2) {
          if (i % 2 == 0) {
            s[i]--;
          } else {
            s[i]++;
          }
        }
      }
      cout << cn1 << endl << s << endl;
    } else {
      for (int i = 0; i < n; i++) {
        if (s[i] - 'A' == i % 2) {
          if (i % 2 == 0) {
            s[i]++;
          } else {
            s[i]--;
          }
        }
      }
      cout << cn2 << endl << s << endl;
    }
    return 0;
  }
  for (int i = 1; i < n - 1; i++) {
    if (s[i] == s[i - 1] && s[i] == s[i + 1]) {
      change(i);
      ans++;
    }
  }
  for (int i = 1; i < n; i++) {
    if (s[i] == s[i - 1]) {
      change(i);
      ans++;
    }
  }
  cout << ans << endl << s << endl;
  return 0;
}