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;
long long n, k;
string s;
long long Diff(string x, string y) {
  long long res = 0;
  for (long long i = 0; i < n; i++) res += (x[i] != y[i]);
  return res;
}
int main() {
  cin >> n >> k >> s;
  if (k == 2) {
    string A1 = "A", A2 = "B";
    for (long long i = 1; i < n; i++) {
      if (i % 2 > 0) {
        A1 += "B";
        A2 += "A";
      } else {
        A1 += "A";
        A2 += "B";
      }
    }
    cout << min(Diff(s, A1), Diff(s, A2)) << endl;
    if (Diff(s, A1) < Diff(s, A2))
      cout << A1;
    else
      cout << A2;
    return 0;
  } else {
    long long B = 0;
    for (long long i = 0; i < n; i++) {
      if (s[i] == s[i + 1]) {
        B++;
        char c = 'A';
        while (c == s[i] || c == s[i + 2]) {
          c++;
        }
        s[i + 1] = c;
      }
    }
    cout << B << endl << s;
  }
  return 0;
}