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 alp[30], map[520000];
int main(void) {
  int i, j, n, k, cnt;
  scanf("%d%d", &n, &k);
  cnt = 0;
  scanf("%s", map);
  if (k != 2) {
    alp[0] = 'A';
    for (i = 1; i < 26; i++) alp[i] = alp[i - 1] + 1;
    for (i = 1; i < n; i++) {
      if (map[i] == map[i - 1]) {
        for (j = 0; j < 26; j++) {
          if (map[i - 1] != alp[j] && map[i + 1] != alp[j]) {
            cnt++;
            map[i] = alp[j];
            break;
          }
        }
      }
    }
  } else {
    int sw = 0;
    for (i = 0; i < n; i++) {
      if (map[i] == 'A' && i % 2 == 1)
        sw++;
      else if (map[i] == 'A' && i % 2 == 0)
        sw--;
    }
    if (sw >= 0) {
      for (i = 0; i < n; i++) {
        if (i % 2 == 1 && map[i] != 'A') {
          cnt++;
          map[i] = 'A';
        } else if (i % 2 == 0 && map[i] == 'A') {
          cnt++;
          map[i] = 'B';
        }
      }
    } else {
      for (i = 0; i < n; i++) {
        if (i % 2 == 1 && map[i] == 'A') {
          cnt++;
          map[i] = 'B';
        } else if (i % 2 == 0 && map[i] == 'B') {
          cnt++;
          map[i] = 'A';
        }
      }
    }
  }
  printf("%d\n%s\n", cnt, map);
  return 0;
}