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(void) {
  int n, k, i, p1 = 0, p2 = 0;
  string s;
  cin >> n >> k >> s;
  if (k == 2) {
    for (int i = 0; i < n; i++) {
      if (s[i] - 'A' != i % 2)
        p1++;
      else
        p2++;
    }
    cout << min(p1, p2) << endl;
    if (p1 < p2) {
      for (int i = 0; i < n; i++) {
        cout << char('A' + i % 2);
      }
    } else {
      for (int i = 0; i < n; i++) {
        cout << char('A' + 1 - (i % 2));
      }
    }
  } else {
    string orig = s;
    for (int i = 1; i < n; i++) {
      if (s[i] == s[i - 1]) {
        p1++;
        s[i] = 'A';
        while (s[i] == s[i - 1] || s[i] == s[i + 1]) {
          s[i]++;
        }
      }
    }
    cout << p1 << endl << s;
  }
  return 0;
}