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.Arrays;
import java.util.Scanner;

public class ColorStripe {

	static int[][] memo;
	static char[][] path;
	static int n , k;
	static String s;
	static int INF = (int)(1e9);
	static int solve(int idx , int prev)
	{
		if(idx == n)
			return 0;
		int cur = s.charAt(idx)-'A'+1;

		if(memo[idx][prev]!=-1)
			return memo[idx][prev];

		int ans = INF;
		char ch = '_';
		if(cur!=prev)
		{
			ans = Math.min(ans, solve(idx+1,cur));
			ch =(char)( cur+'A'-1);
		}
		for(int i=1;i<=Math.min(k, 3);i++)
			if(i!=prev)
			{
				int sol = 1+solve(idx+1,i);
				if(sol<ans)
				{
					ans = sol;
					ch = (char)(i+'A'-1);
					ans = Math.min(ans, 1+solve(idx+1,i));
				}
			}
		path[idx][prev] = ch;
		return memo[idx][prev] = ans; 
	}

	/*static void print(int idx , int prev)
	{
		if(idx == n)
			return ;
		int cur = s.charAt(idx)-'A'+1;
		if(cur!=prev)
			if(solve(idx+1,cur) == memo[idx][prev])
			{
				sb.append((char)(cur+'A'-1));
				print(idx+1,cur);
				return;
			}
		for(int i=1;i<=Math.min(k, 3);i++)
			if(i!=prev)
			{

				if(1+solve(idx+1,i) == memo[idx][prev])
				{
					sb.append((char)(i+'A'-1));
					print(idx+1,(i));
					break;
				}
			}
		return;
	}
	*/
	static StringBuilder sb = new StringBuilder();

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		k = sc.nextInt();
		s = sc.next();
		memo = new int[n+2][k+1];
		for (int i = 0; i < memo.length; i++) {
			Arrays.fill(memo[i], -1);
		}
		path= new char[n+2][k+1];
		int start = n;
		while(start>0)
		{
			for(int i=0;i<=k;i++)
				solve(start,i);
			start-=1000;
		}
		System.out.println(solve(0,0));
		int last = 0;
		for(int i = 0;i<n;i++)
		{
			sb.append(path[i][last]);
			last = path[i][last]-'A'+1;
		}
		
		System.out.println(sb);
		sc.close();
	}

}