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 static java.lang.Math.*;
import java.util.*;
import java.io.*;

public class C {

	public void solve() throws Exception {
		
		int n = nextInt(), k = nextInt();
		String s = nextLine();
		if (k==2) {
			char[] c = s.toCharArray();
			int cntA = 0, cntB = 0;
			for (int i=0; i<n; i+=2) if (c[i]=='B') cntA++;
			for (int i=1; i<n; i+=2) if (c[i]=='A') cntA++;
			for (int i=0; i<n; i+=2) if (c[i]=='A') cntB++;
			for (int i=1; i<n; i+=2) if (c[i]=='B') cntB++;
			if (cntA<cntB) {
				println(cntA);
				for (int i=0; i<n; ++i) print(i%2==0 ? 'A':'B');
			} else {
				println(cntB);
				for (int i=0; i<n; ++i) print(i%2==0 ? 'B':'A');
			}
			return;
		}
		
		char[] c = ('.'+s+'.').toCharArray();
		int cnt = 0;
		int start = c[1]==c[2] ? 1:2;
		for (int i=start; i<n; ++i) {
			if (c[i-1]==c[i] || c[i]==c[i+1]) {
				cnt++;
				for (int j=0; j<k; ++j) {
					char ch = (char)('A'+j);
					if (ch!=c[i] && ch!=c[i+2]) {
						c[i+1]=ch;
						break;
					}
				}
			}
		}
		
		println(cnt);
		for (int i=1; i<=n; ++i) print(c[i]);
		
	}

	

	////////////////////////////////////////////////////////////////////////////
	
	boolean showDebug = true;
	static boolean useFiles = false;
	static String inFile = "input.txt";
	static String outFile = "output.txt";

	double EPS = 1e-7;
	int INF = Integer.MAX_VALUE;
	long INFL = Long.MAX_VALUE;
	double INFD = Double.MAX_VALUE;

	
	int absPos(int num) {
		return num<0 ? 0:num;
	}
	long absPos(long num) {
		return num<0 ? 0:num;
	}
	double absPos(double num) {
		return num<0 ? 0:num;
	}
	
	int min(int... nums) {
		int r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	int max(int... nums) {
		int r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	long minL(long... nums) {
		long r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	long maxL(long... nums) {
		long r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	double minD(double... nums) {
		double r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]<r) r=nums[i];
		return r;
	}
	double maxD(double... nums) {
		double r = nums[0];
		for (int i=1; i<nums.length; ++i)
			if (nums[i]>r) r=nums[i];
		return r;
	}
	
	long sumArr(int[] arr) {
		long res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}
	long sumArr(long[] arr) {
		long res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}
	double sumArr(double[] arr) {
		double res = 0;
		for (int i=0; i<arr.length; ++i)
			res+=arr[i];
		return res;
	}

	long partsFitCnt(long partSize, long wholeSize) {
		return (partSize+wholeSize-1)/partSize;
	}

	boolean odd(long num) {
		return (num&1)==1;
	}
	
	boolean hasBit(int num, int pos) {
		return (num&(1<<pos))>0;
	}

	boolean isLetter(char c) {
		return (c>='a' && c<='z') || (c>='A' && c<='Z');
	}
	boolean isLowercase(char c) {
		return (c>='a' && c<='z');
	}
	boolean isUppercase(char c) {
		return (c>='A' && c<='Z');
	}
	boolean isDigit(char c) {
		return (c>='0' && c<='9');
	}
	
	boolean charIn(String chars, String s) {
		if (s==null) return false;
		if (chars==null || chars.equals("")) return true;
		for (int i=0; i<s.length(); ++i)
			for (int j=0; j<chars.length(); ++j)
				if (chars.charAt(j)==s.charAt(i)) return true;
		return false;
	}
	
	String stringn(String s, int n) {
		if (n<1 || s==null) return "";
		StringBuilder sb = new StringBuilder(s.length()*n);
		for (int i=0; i<n; ++i) sb.append(s);
		return sb.toString();
	}
	String str(Object o) {
		if (o==null) return "";
		return o.toString();
	}


	long timer = System.currentTimeMillis();
	void startTimer() {
		timer = System.currentTimeMillis();
	}
	void stopTimer() {
		System.err.println("time: "+(System.currentTimeMillis()-timer)/1000.0);
	}


	static class InputReader {
		private byte[] buf;
		private int bufPos = 0, bufLim = -1;
		private InputStream stream;
		public InputReader(InputStream stream, int size) {
			buf = new byte[size];
			this.stream = stream;
		}
		private void fillBuf() throws IOException {
			bufLim = stream.read(buf);
			bufPos = 0;
		}
		char read() throws IOException {
			if (bufPos>=bufLim) fillBuf(); 
			return (char)buf[bufPos++];
		}
		boolean hasInput() throws IOException {
			if (bufPos>=bufLim) fillBuf();
			return bufPos<bufLim;
		}
	}
	
	static InputReader inputReader;
	static BufferedWriter outputWriter;

	char nextChar() throws IOException {
		return inputReader.read();
	}
	char nextNonWhitespaceChar() throws IOException {
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		return c;
	}
	String nextWord() throws IOException {
		StringBuilder sb = new StringBuilder();
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		while (c>' ') {
			sb.append(c);
			c = inputReader.read();
		}
		return new String(sb);
	}
	String nextLine() throws IOException {
		StringBuilder sb = new StringBuilder();
		char c = inputReader.read();
		while (c<=' ') c=inputReader.read();
		while (c!='\n' && c!='\r') {
			sb.append(c);
			c = inputReader.read();
		}
		return new String(sb);
	}
	int nextInt() throws IOException {
		int r = 0;
		char c = nextNonWhitespaceChar();
		boolean neg = false;
		if (c=='-') neg=true;
		else r=c-48;
		c = nextChar();
		while (c>='0' && c<='9') {
			r*=10;
			r+=c-48;
			c=nextChar();
		}
		return neg ? -r:r;
	}
	long nextLong() throws IOException {
		long r = 0;
		char c = nextNonWhitespaceChar();
		boolean neg = false;
		if (c=='-') neg=true;
		else r = c-48;
		c = nextChar();
		while (c>='0' && c<='9') {
			r*=10L;
			r+=c-48L;
			c=nextChar();
		}
		return neg ? -r:r;
	}
	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextWord());
	}
	int[] nextArr(int size) throws NumberFormatException, IOException {
		int[] arr = new int[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextInt();
		return arr;
	}
	long[] nextArrL(int size) throws NumberFormatException, IOException {
		long[] arr = new long[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextLong();
		return arr;
	}
	double[] nextArrD(int size) throws NumberFormatException, IOException {
		double[] arr = new double[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextDouble();
		return arr;
	}
	String[] nextArrS(int size) throws NumberFormatException, IOException {
		String[] arr = new String[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextWord();
		return arr;
	}
	char[] nextArrCh(int size) throws IOException {
		char[] arr = new char[size];
		for (int i=0; i<size; ++i)
			arr[i] = nextNonWhitespaceChar();
		return arr;
	}
	char[][] nextArrCh(int rows, int columns) throws IOException {
		char[][] arr = new char[rows][columns];
		for (int i=0; i<rows; ++i)
			for (int j=0; j<columns; ++j)
				arr[i][j] = nextNonWhitespaceChar();
		return arr;
	}
	char[][] nextArrChBorders(int rows, int columns, char border) throws IOException {
		char[][] arr = new char[rows+2][columns+2];
		for (int i=1; i<=rows; ++i)
			for (int j=1; j<=columns; ++j)
				arr[i][j] = nextNonWhitespaceChar();
		for (int i=0; i<columns+2; ++i) {
			arr[0][i] = border;
			arr[rows+1][i] = border;
		}
		for (int i=0; i<rows+2; ++i) {
			arr[i][0] = border;
			arr[i][columns+1] = border;
		}
		return arr;
	}

	void printf(String format, Object... args) throws IOException {
		outputWriter.write(String.format(format, args));
	}
	void print(Object o) throws IOException {
		outputWriter.write(o.toString());
	}
	void println(Object o) throws IOException {
		outputWriter.write(o.toString());
		outputWriter.newLine();
	}
	void print(Object... o) throws IOException {
		for (int i=0; i<o.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(o[i].toString());
		}
	}
	void println(Object... o) throws IOException {
		print(o);
		outputWriter.newLine();
	}
	void printn(Object o, int n) throws IOException {
		String s = o.toString();
		for (int i=0; i<n; ++i) {
			outputWriter.write(s);
			if (i!=n-1) outputWriter.write(' ');
		}
	}
	void printnln(Object o, int n) throws IOException {
		printn(o, n);
		outputWriter.newLine();
	}
	void printArr(int[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Integer.toString(arr[i]));
		}
	}
	void printArr(long[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Long.toString(arr[i]));
		}
	}
	void printArr(double[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(Double.toString(arr[i]));
		}
	}
	void printArr(String[] arr) throws IOException {
		for (int i=0; i<arr.length; ++i) {
			if (i!=0) outputWriter.write(' ');
			outputWriter.write(arr[i]);
		}
	}
	void printlnArr(int[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(long[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(double[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void printlnArr(String[] arr) throws IOException {
		printArr(arr);
		outputWriter.newLine();
	}
	void halt(Object... o) throws IOException {
		if (o.length!=0) println(o);
		outputWriter.flush(); outputWriter.close();
		System.exit(0);
	}
	
	void debug(Object... o) {
		if (showDebug) System.err.println(Arrays.deepToString(o));
	}


	public static void main(String[] args) throws Exception {
		Locale.setDefault(Locale.US);
		if (!useFiles) {
			inputReader = new InputReader(System.in, 1<<16);
			outputWriter = new BufferedWriter(new OutputStreamWriter(System.out), 1<<16);
		} else {
			inputReader = new InputReader(new FileInputStream(new File(inFile)), 1<<16);
			outputWriter = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(new File(outFile))), 1<<16);
		}
		new C().solve();
		outputWriter.flush(); outputWriter.close();
	}
}