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;
int n, k;
char s[500010], sa[500010] = {0}, sb[500010] = {0};
int main() {
  scanf("%d%d%s", &n, &k, s);
  if (k == 2) {
    int a = 0, b = 0, c = 'A';
    for (int i = 0; i < n; ++i) {
      sa[i] = c;
      if (s[i] != c) ++a;
      c = c == 'A' ? 'B' : 'A';
    }
    c = 'B';
    for (int i = 0; i < n; ++i) {
      sb[i] = c;
      if (s[i] != c) ++b;
      c = c == 'A' ? 'B' : 'A';
    }
    if (a < b)
      printf("%d\n%s\n", a, sa);
    else
      printf("%d\n%s\n", b, sb);
  } else {
    int ans = 0;
    for (int i = 0; i < n - 1; ++i) {
      if (s[i] == s[i + 1]) {
        ++ans;
        int c = 'A';
        while (c == s[i] || c == s[i + 2]) ++c;
        s[i + 1] = c;
      }
    }
    printf("%d\n%s\n", ans, s);
  }
  return 0;
}