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 str[500005], ch;
int main() {
  int l, i, j, k, r;
  while (scanf("%d%d", &l, &k) != EOF) {
    scanf("%s", str);
    l = strlen(str);
    if (k == 2) {
      int ans1 = 0, ans2 = 0;
      for (i = 0; i < l; i++)
        if ((i % 2 == 0 && str[i] == 'A') || (i % 2 == 1 && str[i] == 'B'))
          ans1++;
      for (i = 0; i < l; i++)
        if ((i % 2 == 0 && str[i] == 'B') || (i % 2 == 1 && str[i] == 'A'))
          ans2++;
      if (ans1 > ans2) {
        printf("%d\n", ans2);
        for (i = 0; i < l; i++)
          if (i % 2 == 0)
            printf("A");
          else
            printf("B");
      } else {
        printf("%d\n", ans1);
        for (i = 0; i < l; i++)
          if (i % 2 == 0)
            printf("B");
          else
            printf("A");
      }
      puts("");
      continue;
    }
    for (j = i = 1; i < l; i++) {
      if (str[i] == str[i - 1]) {
        for (r = 0; r < 3; r++) {
          ch = 'A' + r;
          if (ch != str[i - 1] && ch != str[i + 1]) {
            str[i] = ch;
            break;
          }
        }
        j++;
      }
    }
    printf("%d\n", j - 1);
    puts(str);
  }
  return 0;
}