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>
int len;
char a[500010];
int main() {
  scanf("%d", &len);
  int k;
  scanf("%d", &k);
  int nub = 0;
  scanf("%s", a);
  len = 0;
  for (len = 0; a[len] != 0; len++)
    ;
  if (k != 2)
    for (int i = 1; i < len; i++) {
      if (a[i] == a[i - 1]) {
        for (int j = 'A'; j <= 'Z'; j++) {
          if (j != a[i + 1] && j != a[i - 1]) {
            nub++;
            a[i] = j;
            break;
          }
        }
      }
    }
  else {
    int sum1 = 0;
    int sum2 = 0;
    for (int i = 0; i < len; i++)
      if (a[i] == 'A' + (i % 2))
        sum1++;
      else
        sum2++;
    if (sum2 < sum1) {
      printf("%d\n", sum2);
      for (int i = 0; i < len; i++) printf("%c", 'A' + (i % 2));
    } else {
      printf("%d\n", sum1);
      for (int i = 0; i < len; i++) printf("%c", 'A' + ((i + 1) % 2));
    }
    return 0;
  }
  printf("%d\n%s", nub, a);
  return 0;
}