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 n, kl;
int a[510001];
int f[510001][50];
int s[510001][50];
int ans, pos;
char q[510001];
int main() {
  int i, j, k;
  int now;
  char c;
  scanf("%d%d", &n, &kl);
  getchar();
  for (i = 1; i <= n; i++) {
    c = getchar();
    a[i] = c - 'A';
  }
  for (i = 1; i <= n; i++) {
    for (j = 0; j < kl; j++) {
      f[i][j] = 0x7fffffff;
    }
  }
  f[1][a[1]] = 0;
  for (i = 1; i <= n; i++) {
    for (j = 0; j < kl; j++) {
      for (k = 0; k < kl; k++) {
        if (k != j && f[i - 1][k] != 0x7fffffff) {
          now = f[i - 1][k] + (j == a[i] ? 0 : 1);
          if (now < f[i][j]) {
            f[i][j] = now;
            s[i][j] = k;
          }
        }
      }
    }
  }
  ans = 0x7fffffff;
  for (i = 0; i < kl; i++) {
    if (f[n][i] < ans) {
      ans = f[n][i];
      pos = i;
    }
  }
  for (i = n; i >= 1; i--) {
    q[i - 1] = pos + 'A';
    pos = s[i][pos];
  }
  printf("%d\n", ans);
  puts(q);
  return 0;
}