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[500005];
int n, k, p1, p2;
int main(void) {
  int i;
  scanf("%d%d%s", &n, &k, s);
  if (k == 2) {
    for (i = 0; i < n; i++) {
      if (s[i] - 'A' != i % 2)
        p1++;
      else
        p2++;
    }
    printf("%d\n", p1 < p2 ? p1 : p2);
    if (p1 > p2)
      for (i = 0; i < n; i++) printf("%c", 'A' + (i + 1) % 2);
    else
      for (i = 0; i < n; i++) printf("%c", 'A' + i % 2);
    printf("\n");
  } else {
    int ans = 0;
    for (i = 2; i < n; i++) {
      if (s[i - 2] == s[i - 1]) {
        s[i - 1] = 'A';
        while (s[i - 1] == s[i] || s[i - 2] == s[i - 1]) s[i - 1]++;
        ans++;
      }
    }
    if (s[n - 2] == s[n - 1]) {
      s[n - 1] = 'A';
      while (s[n - 2] == s[n - 1]) s[n - 1]++;
      ans++;
    }
    printf("%d\n%s\n", ans, s);
  }
  return 0;
}