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.Scanner;

public class ColorStripe {
	public static void specialCase(String s)
	{
		//startWithA
		StringBuilder sbA = new StringBuilder();
		int countA = 0;
		for (int i=0;i<s.length();i++)
		{
			char c = (i%2==0)?'A':'B';
			sbA.append(c);
			if (c!=s.charAt(i))
				countA++;
		}
		StringBuilder sbB = new StringBuilder();
		int countB = 0;
		for (int i=0;i<s.length();i++)
		{
			char c = (i%2==0)?'B':'A';
			sbB.append(c);
			if (c!=s.charAt(i))
				countB++;
		}
		if (countA<countB)
		{
			System.out.println(countA);
			System.out.println(sbA);
			return;
		}
		System.out.println(countB);
		System.out.println(sbB);
	}
	public static void main(String args[])
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		sc.nextLine();
		String s = sc.nextLine();
		int count=0;
		int nums[] = new int[n];
		for (int i=0;i<n;i++)
			nums[i] = s.charAt(i)-'A';
		if (k==2)
		{
			specialCase(s);
			return;
		}
		for (int i=1;i<n;i++)
		{
			if (nums[i]==nums[i-1])
			{
				count++;
				if (i==n-1)
				{
					if (nums[i-1]==0)
						nums[i] = 1;
					else
						nums[i] = 0;
					continue;
				}
				for (int j=0;j<k;j++)
				{
					if (j!=nums[i-1] && j!=nums[i+1])
					{
						nums[i] = j;
						break;
					}
				}
			}
		}
		StringBuilder sb = new StringBuilder();
		System.out.println(count);
		for (int i=0;i<n;i++)
			sb.append((char) (nums[i]+'A')+"");
		System.out.println(sb);
	}
}