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 JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;
public class cf219c {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    int n = in.nextInt();
    int k = in.nextInt();
    String s = in.next().trim();
    if(k == 2) {
      int ans1 = 0, ans2 = 0;
      for(int i=0; i<n; i++)
        if(s.charAt(i)-'A' == i%2) 
          ans1++;
      for(int i=0; i<n; i++)
        if(s.charAt(i)-'A' != i%2) 
          ans2++;
      if(ans1 < ans2) {
        out.println(ans1);
        for(int i=0; i<n; i++)
          out.print((char)('A'+(i+1)%2));
      }
      else {
        out.println(ans2);
        for(int i=0; i<n; i++)
          out.print((char)('A'+i%2));  
      }
      out.close();
      return;
    }
    ArrayList<Integer> len = new ArrayList<Integer>();
    ArrayList<Character> ch = new ArrayList<Character>();
    int last = 0;
    for(int i=0; i<=n; i++) {
      if(i == n || s.charAt(i) != s.charAt(last)) {
        len.add(i-last);
        ch.add(s.charAt(last));
        last = i;
      }
    }
    StringBuilder sb = new StringBuilder();
    int ans = 0;
    for(int i=0; i<len.size(); i++) {
      char here = ch.get(i);
      char other = 'A';
      while(other == here || (i < len.size() -1 && other == ch.get(i+1)))
        other++;
      ans += len.get(i)/2;
      for(int j=0; j<len.get(i); j++)
        if(j%2 == 0)
          sb.append(here);
        else
          sb.append(other);
    }
    out.println(ans);
    out.println(sb.toString());
    out.close();
  }
}