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;
  cin >> n >> k;
  int d = 0, ans = 0;
  char a[5000005];
  cin >> a;
  if (k == 2) {
    for (int i = 0; i < n; i++) {
      if (a[i] == 'A' + (i & 1)) d++;
    }
    if (n - d < d)
      ans = n - d;
    else
      ans = d;
    for (int i = 0; i < n; i++) {
      a[i] = 'A' + (((d == ans) + i) & 1);
    }
  } else {
    for (int i = 0; i < n; i++) {
      if (a[i] == a[i + 1]) {
        ans++;
        char c = 'A';
        while (c == a[i] || c == a[i + 2]) {
          c++;
        }
        a[i + 1] = c;
      }
    }
  }
  cout << ans << endl << a;
}