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 n, m;
  while (~scanf("%d%d", &n, &m)) {
    string s;
    cin >> s;
    int i;
    if (m == 2) {
      string a, b;
      a = b = "";
      for (i = 0; i < s.size(); i++)
        if (i & 1)
          a += 'A', b += 'B';
        else
          b += 'A', a += 'B';
      int l = 0, r = 0;
      for (i = 0; i < s.size(); i++) {
        if (s[i] != a[i]) l++;
        if (s[i] != b[i]) r++;
      }
      int ll = min(l, r);
      printf("%d\n%s\n", ll, ll == l ? a.c_str() : b.c_str());
    } else {
      int t = 0;
      for (i = 0; i < s.size() - 1; i++)
        if (s[i] == s[i + 1]) {
          char c = 'A';
          if (s[i] == c || s[i + 2] == c) c++;
          if (s[i] == c || s[i + 2] == c) c++;
          t++;
          s[i + 1] = c;
        }
      printf("%d\n%s\n", t, s.c_str());
    }
  }
}