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>
int min(int a, int b) {
  if (a < b) {
    return a;
  } else {
    return b;
  }
}
int d[107][107][20], mod = 100000000, a[15], r[50007][20];
char c[500007], u, x;
void solve(int n) {
  int i, j, y = 1, s1 = 0, s2 = 0, k, s = 0;
  scanf("%d", &k);
  gets(c);
  gets(c);
  if (k == 2) {
    u = 'A';
    for (i = 0; i < n; i++) {
      if (c[i] != u) {
        s1++;
      }
      u = u + y;
      y = y * (-1);
      if (c[i] != u) {
        s2++;
      }
    }
    if (s1 < s2) {
      printf("%d\n", s1);
      y = 1;
      u = 'A';
      for (i = 0; i < n; i++) {
        printf("%c", u);
        u = u + y;
        y = y * (-1);
      }
    } else {
      printf("%d\n", s2);
      y = 1;
      u = 'B';
      for (i = 0; i < n; i++) {
        printf("%c", u);
        u = u - y;
        y = y * (-1);
      }
    }
    return;
  }
  for (i = 1; i < n; i++) {
    if (c[i] == c[i - 1]) {
      for (x = 'A'; x <= 'A' + k - 1; x++) {
        if (c[i + 1] != x && c[i - 1] != x && c[i] == c[i - 1]) {
          c[i] = x;
          s++;
        }
      }
    }
  }
  printf("%d\n", s);
  for (i = 0; i < n; i++) {
    printf("%c", c[i]);
  }
}
int main() {
#pragma comment(linker, "/STACK:67108864")
  int n;
  while (scanf("%d", &n) != EOF) {
    solve(n);
  }
  return 0;
}