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.util.*;
public class A {
    static void print (char s[], int len) {
        for (int i = 0; i < len; i ++) 
            System.out.print (s[i]);
        System.out.println ();
    }
    public static void main (String a[]) {
        Scanner in = new Scanner (System.in);
        
        int len = in.nextInt(), k = in.nextInt();

        char s[] = in.next().toCharArray();
        //System.out.println (s);
        if (k == 2) {
            char s1[] = new char[len];
            char s2[] = new char[len];
            for (int i = 0; i < len; i ++) {
                s1[i] = (char)('A' + (i & 1)); s2[i] = (char)('A' + ((i + 1) & 1));
                //System.out.println (s1 + "---" + s2);
            }
            int c1 = 0, c2 = 0;
            for (int i = 0; i < len; i ++) {
                c1 += (s1[i] == s[i] ? 0 : 1);
                c2 += (s2[i] == s[i] ? 0 : 1);
            }
            if (c1 < c2) {
                System.out.println (c1 + "\n"); print (s1, len);
            }
            else {
                System.out.println (c2 + "\n"); print (s2, len);
            }
        } 
        else {
            int cnt = 0;
            for (int i = 1; i < len; i ++){
                if (s[i - 1] == s[i]) {
                    cnt ++;
                    for (int j = 0; j < k; j ++) {
                        if (s[i - 1] != (char)(j + 'A') && ((i + 1 < len && s[i + 1] != (char)(j + 'A'))
                                || i + 1 == len)) {
                            s[i] = (char)(j + 'A');
                            break;
                        }
                    }
                }
                
            }
            System.out.println (cnt);
            print (s, len);
        }       
    }
}