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:
/**
 * DA-IICT
 * Author : PARTH PATEL
 */
import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class C219 {

	public static int mod = 1000000007;
	static FasterScanner in = new FasterScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int maxn = (int) (1e5 + 2);
	static ArrayList<Integer>[] adjacencylist = new ArrayList[maxn];
	static boolean[] visited = new boolean[maxn];
	static int[] color = new int[maxn];

	public static void main(String[] args) {

		int n=in.nextInt();
		int k=in.nextInt();
		int ans=0;
		StringBuilder sb=new StringBuilder(in.nextLine());
		char[] carr=sb.toString().toCharArray();
		if(n==1)
		{
			System.out.println("0");
			System.out.println(sb.toString());
			return;
		}
		if(k>2)
		{
			for(int i=1;i<n-1;i++)
			{
				if(carr[i]==carr[i-1])
				{
					for(char c='A';c<='A'+k;c++)
					{
						if(carr[i-1]!=c && carr[i+1]!=c)
						{
							ans++;
							carr[i]=c;
							break;
						}
					}
				}
			}
			if(carr[n-1]==carr[n-2])
			{
				for(char c='A';c<='A'+k;c++)
				{
					if(carr[n-2]!=c)
					{
						ans++;
						carr[n-1]=c;
						break;
					}
				}
			}
			out.println(ans);
			for(int i=0;i<n;i++)
				out.print(carr[i]);
		}
		else
		{
			StringBuilder sb1=new StringBuilder();
			StringBuilder sb2=new StringBuilder();
			for(int i=0;i<n;i++)
			{
				if(i%2==0)
				{
					sb1.append("A");
					sb2.append("B");
				}
				else
				{
					sb1.append("B");
					sb2.append("A");
				}
			}
			int count1=0,count2=0;
			for(int i=0;i<n;i++)
			{
				if(sb1.charAt(i)!=sb.charAt(i))
					count1++;
				if(sb2.charAt(i)!=sb.charAt(i))
					count2++;
			}
			if(count1<count2)
			{
				out.println(count1);
				out.println(sb1.toString());
			}
			else
			{
				out.println(count2);
				out.println(sb2.toString());
			}
		}
		out.close();

	}

	public static void dfs(int vertex) {
		visited[vertex] = true;
		for (int i : adjacencylist[vertex]) {
			if (!visited[i]) {
				dfs(i);
			}
		}
	}

	/////////////////SEGMENT TREE (BUILD-UPDATE-QUERY)/////////////////////////////
	/////////////////UPDATE FOLLOWING METHODS AS PER NEED//////////////////////////
	/*
	public static void buildsegmenttree(int node,int start,int end)
	{
		if(start==end)
		{
			// Leaf node will have a single element
			segmenttree[node]=arr[start];
		}
		else
		{
			int mid=start+(end-start)/2;
			// Recurse on the left child
			buildsegmenttree(2*node, start, mid);
			// Recurse on the right child
			buildsegmenttree(2*node+1, mid+1, end);
			// Internal node will have the sum of both of its children
			segmenttree[node]=segmenttree[2*node]+segmenttree[2*node+1];
		}
	}
	
	public static void updatesegmenttree(int node,int start,int end,int idx,int val)
	{
		if(start==end)
		{
			//Leaf Node
			arr[idx]+=val;
			segmenttree[node]+=val;
		}
		else
		{
			int mid=start+(end-start)/2;
			if(start<=idx && idx<=mid)
			{
				// If idx is in the left child, recurse on the left child
				updatesegmenttree(2*node, start, mid, idx, val);
			}
			else
			{
				// if idx is in the right child, recurse on the right child
				updatesegmenttree(2*node+1, mid+1, end, idx, val);
			}
			// Internal node will have the sum of both of its children
			segmenttree[node]=segmenttree[2*node]+segmenttree[2*node+1];
		}
	}
	
	public static long querysegmenttree(int node,int start,int end,int l,int r)
	{
		if(r<start || end<l)
		{
			// range represented by a node is completely outside the given range
			return 0;
		}
		if(l <= start && end <= r)
	    {
	        // range represented by a node is completely inside the given range
	        return segmenttree[node];
	    }
		// range represented by a node is partially inside and partially outside the given range
		int mid=start+(end-start)/2;
		long leftchild=querysegmenttree(2*node, start, mid, l, r);
		long rightchild=querysegmenttree(2*node+1, mid+1, end, l, r);
		return (leftchild+rightchild);
	}
	*/

	public static long pow(long x, long n, long mod) {
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) {
			if ((n & 1) != 0) {
				res = (res * p % mod);
			}
		}
		return res;
	}

	public static long gcd(long n1, long n2) {
		long r;
		while (n2 != 0) {
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long lcm(long n1, long n2) {
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}

}