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 main(int argc, char** argv) {
  int n, k;
  scanf("%d %d", &n, &k);
  string s;
  cin >> s;
  int res = 0;
  if (k == 2) {
    int fi = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] - 'A' != fi) res++;
      fi = 1 - fi;
    }
    int tmp = 0;
    fi = 1;
    for (int i = 0; i < n; i++) {
      if (s[i] - 'A' != fi) tmp++;
      fi = 1 - fi;
    }
    fi = (res < tmp) ? 0 : 1;
    cout << min(res, tmp) << endl;
    for (int i = 0; i < n; i++) {
      cout << char(fi + 'A');
      fi = 1 - fi;
    }
  } else {
    int res = 0;
    for (int i = 1; i <= n - 1; i++) {
      if (s[i] != s[i - 1]) continue;
      res++;
      for (int j = 0; j < 3; j++)
        if (s[i] - 'A' == j || (i < n - 1 && s[i + 1] - 'A' == j))
          continue;
        else {
          s[i] = char('A' + j);
          break;
        }
    }
    cout << res << endl;
    cout << s;
  }
  return 0;
}