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;
ifstream f("date.in");
int n, k;
char a[10000000], word1[10000000], word2[10000000], aux[10000000];
int fc(char c1, char c2) {
  int idx1 = c1 - 'A' + 1;
  int idx2 = c2 - 'A' + 1;
  for (int i = 1; i <= k; i++)
    if (i != idx1 && i != idx2) return i;
  return -1;
}
int c;
int main() {
  cin >> n >> k;
  cin >> a;
  strcpy(aux, a);
  if (n == 2) {
    if (a[0] == a[1])
      cout << 1 << '\n' << "AB";
    else {
      cout << 0 << '\n';
      cout << a;
    }
    return 0;
  }
  for (int i = 1; i < n; i++) {
    char c1 = a[i - 1];
    char c2 = a[i + 1];
    if (a[i] == c1) {
      int rez = fc(c1, c2);
      if (rez == -1) {
        int m1 = 0, m2 = 0;
        for (int j = 0; j < n; j++) {
          if (j % 2 == 0)
            word1[j] = 'A';
          else
            word1[j] = 'B';
          if (j % 2 == 0)
            word2[j] = 'B';
          else
            word2[j] = 'A';
          if (aux[j] != word1[j]) {
            m1++;
          }
          if (aux[j] != word2[j]) {
            m2++;
          }
        }
        word1[n] = word2[n] = '\0';
        if (m1 > m2) {
          cout << m2 << '\n';
          cout << word2;
        } else {
          cout << m1 << '\n';
          cout << word1;
        }
        return 0;
      }
      c++;
      a[i] = 'A' + rez - 1;
    }
  }
  cout << c << '\n';
  cout << a;
}