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() {
  string s;
  int n, k, i, j;
  char ch1;
  cin >> n >> k;
  cin >> s;
  int cnt = 0, cnt1 = 0;
  if (k == 2) {
    int f = 0;
    string s1 = "", s2 = "";
    for (i = 0; i < n; i++) {
      if (f == 0)
        s1 += 'A';
      else
        s1 += 'B';
      f = 1 - f;
    }
    f = 0;
    for (i = 0; i < n; i++) {
      if (f == 0)
        s2 += 'B';
      else
        s2 += 'A';
      f = 1 - f;
    }
    for (i = 0; i < n; i++) {
      if (s[i] != s1[i]) cnt++;
      if (s[i] != s2[i]) cnt1++;
    }
    if (cnt < cnt1) {
      cout << cnt << endl;
      cout << s1 << endl;
    } else {
      cout << cnt1 << endl;
      cout << s2 << endl;
    }
    return 0;
  }
  for (i = 1; i < n; i++) {
    if (s[i] == s[i - 1]) {
      for (j = 1; j < k + 1; j++) {
        ch1 = char(64 + j);
        if (i + 1 < n) {
          if (ch1 != s[i + 1] && ch1 != s[i]) {
            s[i] = ch1;
            cnt++;
            break;
          }
        } else {
          if (ch1 != s[i]) {
            s[i] = ch1;
            cnt++;
            break;
          }
        }
      }
    }
  }
  cout << cnt << endl;
  cout << s << endl;
  return 0;
}