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:
// package com.company.codeforces;

import java.util.Arrays;
import java.util.Scanner;

public class Solution {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        int k = input.nextInt();
        String s = input.next();
        int count = 0;
        char a[] = s.toCharArray();

        if (k == 2) {
            int ab = 0, ba = 0;
            for (int i = 0; i < n; i++)
                if (i % 2 == 0) {
                    if (a[i] == 'A')
                        ba++;
                    else if (a[i] == 'B')
                        ab++;
                } else {
                    if (a[i] == 'B')
                        ba++;
                    else if (a[i] == 'A')
                        ab++;
                }
           int m = Math.min(ab, ba);
            System.out.println(m);
            for (int i = 0; i < n; i++)
                a[i] = (i % 2 == 0 && ab <= ba || i % 2 == 1 && ab > ba) ? 'A' : 'B';
            System.out.println(a);


        } else {


            for (int i = 1; i < n; i++) {
                if (a[i] == a[i - 1]) {
                    count++;
                    int temp = a[i] - 'A' + 1;


                    int ans = 0;
                    if (i + 1 < n) {
                        int aage = a[i + 1] - 'A' + 1;
                        for (int j = 1; j <= k; j++) {
                            if (j != temp && j != aage) {
                                ans = j;
                                break;
                            }

                        }
                    } else {
                        for (int j = 1; j <= k; j++) {
                            if (j != temp) {
                                ans = j;
                                break;
                            }

                        }
                    }
                    a[i] = (char) (64 + ans);

                }

            }
            System.out.println(count);
       
            System.out.println(a);
        }
    }
}