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;
void solve() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int n, k;
  cin >> n >> k;
  string second;
  cin >> second;
  if (k > 2) {
    int c = 0;
    for (int i = 1; i < n; i++) {
      if (second[i] == second[i - 1]) {
        if (i + 1 < n) {
          int j = 0;
          while (j < k &&
                 ((j + 'A') == second[i - 1] || (j + 'A') == second[i + 1]))
            j++;
          second[i] = j + 'A';
        } else {
          second[i] = ((second[i - 1] - 'A' + 1) % k) + 'A';
        }
        c++;
      }
    }
    cout << c << '\n';
    cout << second << '\n';
    return;
  }
  string t = "A", h = "B";
  for (int i = 1; i < n; i++) {
    if (t[i - 1] == 'A')
      t += 'B';
    else
      t += 'A';
    if (h[i - 1] == 'A')
      h += 'B';
    else
      h += 'A';
  }
  int c1 = 0, c2 = 0;
  for (int i = 0; i < n; i++) {
    if (second[i] != t[i]) c1++;
    if (h[i] != second[i]) c2++;
  }
  cout << min(c1, c2) << '\n';
  if (c1 <= c2)
    cout << t << '\n';
  else
    cout << h << '\n';
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}