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;
char p[500001];
int len, k;
void exchage(char *data, int i, char st, char en) {
  int j, a, b;
  a = st - 'A';
  b = en - 'A';
  for (j = 0; j < k; j++)
    if (j != a && j != b) {
      data[i] = j + 'A';
      return;
    }
}
void slove2() {
  int i, a = 0, b = 0, ans;
  char c = 'A';
  for (i = 0; i < len; i++) {
    if (p[i] == c)
      b++;
    else
      a++;
    if (c == 'A')
      c = 'B';
    else
      c = 'A';
  }
  ans = a < b ? a : b;
  printf("%d\n", ans);
  if (a > b)
    c = 'B';
  else
    c = 'A';
  for (i = 0; i < len; i++) {
    printf("%c", c);
    if (c == 'A')
      c = 'B';
    else
      c = 'A';
  }
  puts("");
}
void slove() {
  int i, ans = 0;
  for (i = 1; i < len - 1; i++) {
    if (p[i - 1] == p[i]) {
      exchage(p, i, p[i - 1], p[i + 1]);
      ans++;
    }
  }
  if (p[len - 1] == p[len - 2]) {
    ans++;
    exchage(p, len - 1, p[len - 2], p[len - 2]);
  }
  printf("%d\n", ans);
  puts(p);
}
int main() {
  while (~scanf("%d %d", &len, &k)) {
    scanf("%s", p);
    if (k == 2)
      slove2();
    else
      slove();
  }
  return 0;
}