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 const AL = 26;
char const A = 'A';
int main() {
  int n, k;
  string s;
  cin >> n >> k >> s;
  int ans = 2e9;
  string ans_string;
  if (k == 2) {
    for (int j = 0; j < k; j++) {
      string tmp;
      int cnt = 0;
      for (int i = 0; i < n; i++) {
        tmp.push_back(char(A + ((i + j) & 1)));
        if (tmp[i] != s[i]) cnt++;
      }
      if (cnt < ans) {
        ans = cnt;
        ans_string = tmp;
      }
    }
  } else {
    ans = 0;
    for (int i = 0; i < n;) {
      int j;
      for (j = i; j < n && s[j] == s[i]; j++)
        ;
      if (j - i + 1 >= 2) {
        if ((j - i) % 2 == 1) {
          for (int k = i + 1; k < j; k += 2) {
            s[k] = (s[i] == A ? 'B' : 'A');
            ans++;
          }
        } else {
          char tmp;
          for (int k = 0; k < 3; k++) {
            if (A + k != s[i] && (j == n || s[j] != A + k)) tmp = A + k;
          }
          for (int k = i + 1; k < j; k += 2) {
            s[k] = tmp;
            ans++;
          }
        }
      }
      i = j;
    }
    ans_string = s;
  }
  cout << ans << endl;
  cout << ans_string;
  return 0;
}