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>
char s[10000009];
char c[] = {'X', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H',
            'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q',
            'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'};
void check(int p, int l, int k) {
  int i = 0;
  for (i = 1; i <= k; i++) {
    if (p < (l - 1)) {
      if (c[i] != s[p - 1] && c[i] != s[p + 1]) {
        s[p] = c[i];
        return;
      }
    } else if (c[i] != s[p - 1]) {
      s[p] = c[i];
      return;
    }
  }
  return;
}
int calc(int k) {
  int l = strlen(s);
  int i = 0;
  int count = 0;
  for (i = 1; i < l; i++) {
    if (s[i] == s[i - 1]) {
      check(i, l, k);
      count++;
    }
  }
  return count;
}
int main() {
  int n, k, i = 0;
  int j = 0, j1 = 0;
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  if (k > 2) {
    printf("%d\n", calc(k));
    printf("%s", s);
  } else {
    for (i = 0; i < n; i++) {
      if (i % 2 == 0) {
        if (s[i] != 'B') j++;
      } else if (s[i] != 'A')
        j++;
    }
    for (i = 0; i < n; i++) {
      if (i % 2 == 0) {
        if (s[i] != 'A') j1++;
      } else if (s[i] != 'B')
        j1++;
    }
    if (j < j1) {
      printf("%d\n", j);
      for (i = 0; i < n; i++)
        if (i % 2 == 0)
          printf("B");
        else
          printf("A");
    } else {
      printf("%d\n", j1);
      for (i = 0; i < n; i++)
        if (i % 2 == 0)
          printf("A");
        else
          printf("B");
    }
  }
  return 0;
}