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.*;
import java.util.*;

public class C {
    public static void main(String[] args) throws Exception {
        new C().solve();
    }
    
    void solve() throws IOException {
        // BufferedReader in = new BufferedReader(new
        // InputStreamReader(System.in));
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        char[] car = sc.next().toCharArray();
        
        
        if (k == 2) {
            // ABAB.... or BABA...
            int count = n * 2;
            char cs = 'A';
            for (int c0 = 'A'; c0 <= 'B'; c0++) {
                int cnt = 0;
                for (int i = 0; i < n; i++) {
                    char c = (char) ((i % 2 == 0) ? c0 : -c0 + 'A' + 'B');
                    if (car[i] != c) {
                        cnt++;
                    }
                }
                if (cnt < count) {
                    count = cnt;
                    cs = (char) c0;
                }
            }
            for (int i = 0; i < n; i++) {
                char c = (char) ((i % 2 == 0) ? cs : -cs + 'A' + 'B');
                car[i] = c;
            }
            System.out.println(count);
            System.out.println(new String(car));
            
        } else {
            int count = 0;
            for (int i = 1; i < n; i++) {
                if (car[i - 1] == car[i]) {
                    count++;
                    car[i]++;
                    if (car[i] == 'A' + k) car[i] = 'A';
                    while (i != n - 1 && car[i] == car[i + 1]) {
                        car[i]++;
                        if (car[i] == 'A' + k) car[i] = 'A';
                    }
                }
            }
            System.out.println(count);
            System.out.println(new String(car));
        }
    }
}










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