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, k, ans = 0, tempans = 0;
  char s[500005], temp[500005], tempa[500005];
  cin >> n >> k >> s;
  if (k == 2) {
    for (int i = 0; i < n; i++) {
      if (i % 2 == 1)
        temp[i] = 'A';
      else
        temp[i] = 'B';
    }
    for (int i = 0; i < n; i++)
      if (s[i] != temp[i]) ans++;
    for (int i = 0; i < n; i++)
      if (i % 2 == 1)
        tempa[i] = 'B';
      else
        tempa[i] = 'A';
    for (int i = 0; i < n; i++)
      if (s[i] != tempa[i]) tempans++;
    if (tempans < ans) {
      ans = tempans;
      for (int i = 0; i < n; i++) s[i] = tempa[i];
    } else
      for (int i = 0; i < n; i++) s[i] = temp[i];
  } else
    for (int i = 0; i + 1 < n; i++) {
      if (s[i] == s[i + 1]) {
        char w = 'A';
        if (w == s[i] or w == s[i + 2]) w++;
        if (w == s[i] or w == s[i + 2]) w++;
        s[i + 1] = w;
        ans++;
      }
    }
  cout << ans << endl;
  cout << s << endl;
}