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 CF219C {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		char[] cc = br.readLine().toCharArray();
		int m;
		if (k == 2) {
			int ab = 0, ba = 0;
			for (int i = 0; i < n; i++)
				if (i % 2 == 0) {
					if (cc[i] == 'A')
						ba++;
					else if (cc[i] == 'B')
						ab++;
				} else {
					if (cc[i] == 'B')
						ba++;
					else if (cc[i] == 'A')
						ab++;
				}
			m = Math.min(ab, ba);
			for (int i = 0; i < n; i++)
				cc[i] = (i % 2 == 0 && ab <= ba || i % 2 == 1 && ab > ba) ? 'A' : 'B';
		} else {
			m = 0;
			for (int i = 1; i < n; i++)
				if (cc[i] == cc[i - 1]) {
					m++;
					while (cc[i] == cc[i - 1] || i + 1 < n && cc[i] == cc[i + 1])
						cc[i] = cc[i] == (char) ('A' + k - 1) ? 'A' : (char) (cc[i] + 1);
				}
		}
		System.out.println(m);
		System.out.println(cc);
	}
}