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;
class Reader {
  char buf[1048576], b;
  int bi, bz;
  void read() {
    if (bi == bz) {
      bi = 0;
      bz = fread(buf, 1, 1048576, stdin);
    }
    b = bz ? buf[bi++] : 0;
  }
  void skip() {
    while (b > 0 && b <= 32) read();
  }

 public:
  Reader() {
    bi = bz = 0;
    read();
  }
  unsigned int nextInt() {
    unsigned int v = 0;
    for (skip(); b > 32; read()) v = v * 10 + b - 48;
    return v;
  }
};
int k;
inline char getLetter(char *p) {
  if (!(*p == 'A' || p[1] == 'A')) return 'A';
  if (!(*p == 'B' || p[1] == 'B')) return 'B';
  return 'C';
}
int main() {
  int n, change = 0, i;
  char s[500005];
  char *p;
  scanf("%d%d%s", &n, &k, s + 1);
  if (k == 1)
    puts("0"), puts(s + 1);
  else if (k == 2) {
    int cn = 0;
    bool dec = false;
    for (i = 1; s[i]; i++) cn += s[i] != 'A' + !(i & 1);
    if (n >= (cn << 1)) dec = true;
    for (i = 1; i <= n; i++) s[i] = 'A' + ((i & 1) ^ dec);
    printf("%d\n%s\n", min(cn, n - cn), s + 1);
  } else {
    *s = 0;
    for (p = s + 1; *p; p++)
      if (*p == p[-1]) {
        change++;
        *p = getLetter(p);
      }
    printf("%d\n%s\n", change, s + 1);
  }
  return 0;
}