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 a[500010];
int n, m;
void chang(int s) {
  if (s == 0) {
    a[s]++;
    if (a[s] >= 'A' + m) a[s] = 'A';
    while (a[s] == a[s + 1]) {
      a[s]++;
      if (a[s] >= 'A' + m) a[s] = 'A';
    }
  } else if (s == n - 1) {
    a[s]++;
    if (a[s] >= 'A' + m) a[s] = 'A';
    while (a[s] == a[s - 1]) {
      a[s]++;
      if (a[s] >= 'A' + m) a[s] = 'A';
    }
  } else {
    a[s]++;
    if (a[s] >= 'A' + m) a[s] = 'A';
    while (a[s] == a[s - 1] || a[s] == a[s + 1]) {
      a[s]++;
      if (a[s] >= 'A' + m) a[s] = 'A';
    }
  }
}
int main() {
  while (~scanf("%d%d", &n, &m)) {
    scanf("%s", a);
    int ans = 0, ans1 = 0;
    if (m == 2) {
      int a1 = 0, a2 = 0, b1 = 0, b2 = 0;
      for (int i = 0; i < n; i++) {
        if (i % 2 == 0) {
          if (a[i] == 'A')
            a1++;
          else
            b1++;
        } else {
          if (a[i] == 'A')
            a2++;
          else
            b2++;
        }
      }
      if ((a2 + b1) > (a1 + b2)) {
        printf("%d\n", a1 + b2);
        for (int i = 0; i < n; i++) {
          if (i % 2 == 0)
            printf("B");
          else
            printf("A");
        }
        printf("\n");
      } else {
        printf("%d\n", a2 + b1);
        for (int i = 0; i < n; i++) {
          if (i % 2 == 0)
            printf("A");
          else
            printf("B");
        }
        printf("\n");
      }
      continue;
    }
    for (int i = 1; i < n; i++) {
      if (a[i] == a[i - 1] && a[i] != a[i + 1])
        chang(i - 1), ans++;
      else if (a[i] == a[i + 1] && a[i] != a[i - 1])
        chang(i + 1), ans++;
      else if (a[i] == a[i + 1] && a[i] == a[i - 1])
        chang(i), ans++;
    }
    printf("%d\n%s\n", ans, a);
  }
  return 0;
}