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;
const int INF = 1000 * 1000 * 1000;
const double EPS = 1e-10;
int hamdist(string a, string b) {
  int res = 0;
  for (int i = 0; i < (a.size()); i++) {
    if (a[i] != b[i]) res++;
  }
  return res;
}
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  int res = 0;
  if (k > 2) {
    for (typeof(1) i = (1); i < (n); i++) {
      if (s[i] == s[i - 1]) {
        for (typeof('A') c = ('A'); c <= ('A' + k); c++) {
          if (c != s[i - 1] && (i + 1 >= n || c != s[i + 1])) {
            s[i] = c;
            res++;
            break;
          }
        }
      }
    }
  } else {
    string ab = "", ba = "";
    for (int i = 0; i < (n); i++) {
      ab += ('A' + i % 2);
      ba += ('A' + (i + 1) % 2);
    }
    if (hamdist(ab, s) < hamdist(ba, s)) {
      res = hamdist(ab, s);
      s = ab;
    } else {
      res = hamdist(ba, s);
      s = ba;
    }
  }
  cout << res << endl << s << endl;
  return 0;
}