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 f(char a) {
  if (a == 'A') return 'B';
  return 'A';
}
int main() {
  int i, j, k = 0, l, mx = 0, a, b, n;
  string s, s1, s2;
  char c1 = 'A', c2 = 'B';
  cin >> a >> b;
  cin >> s;
  n = s.size();
  if (b == 2) {
    for (i = 0; i < n; i++) {
      s1 += c1;
      s2 += c2;
      if (s[i] != c1)
        k++;
      else
        mx++;
      swap(c1, c2);
    }
    if (k < mx)
      cout << k << endl << s1 << endl;
    else
      cout << mx << endl << s2 << endl;
    return 0;
  }
  s += 'p';
  for (i = 1; i < n; i++) {
    if (s[i] == s[i - 1]) {
      for (j = 0; j < b; j++) {
        if (j + 'A' != s[i - 1] && j + 'A' != s[i + 1]) {
          s[i] = j + 'A';
          break;
        }
      }
      k++;
    }
  }
  cout << k << endl << s.substr(0, n) << endl;
  return 0;
}