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 Main {
	InputReader scn;
	PrintWriter out;
	String INPUT = "";

	void solve() {
		int n = scn.nextInt(), k = scn.nextInt();
		StringBuilder str = new StringBuilder(scn.next());
		int[] dp = new int[n];
		if(n == 1) {
			out.println(0);
			out.println(str);
			return;
		}
		if (k > 2) {
			for (int i = 1; i < n - 1; i++) {
				if (str.charAt(i) != str.charAt(i - 1)) {
					dp[i] = dp[i - 1];
				} else {
					for (int j = 0; j < k; j++) {
						char ch = (char) ('A' + j);
						if (str.charAt(i - 1) != ch && str.charAt(i + 1) != ch) {
							str.setCharAt(i, ch);
						}
					}
					dp[i] = dp[i - 1] + 1;
				}
			}
			dp[n - 1] = dp[n - 2];
			if (str.charAt(n - 1) == str.charAt(n - 2)) {
				if(str.charAt(n - 1) == 'A') {
					str.setCharAt(n - 1, 'B');
				} else {
					str.setCharAt(n - 1, 'A');
				}
				dp[n - 1]++;
			}
			out.println(dp[n - 1]);
			out.println(str);
		} else if(k == 2) {
			StringBuilder s1 = new StringBuilder(), s2 = new StringBuilder();
			int x = 0, y = 0;
			for(int i = 0; i < n; i++) {
				if(i % 2 == 0) {
					s1.append('A');
					s2.append('B');
				} else {
					s2.append('A');
					s1.append('B');
				}
				if(str.charAt(i) == s1.charAt(i)) {
					y++;
				} else {
					x++;
				}
			}
			out.println(Math.min(x, y));
			if(x < y) {
				out.println(s1);
			} else {
				out.println(s2);
			}
		} else {
			
		}
	}

	void run() throws Exception {
		boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;
		out = new PrintWriter(System.out);
		scn = new InputReader(onlineJudge);
		long time = System.currentTimeMillis();
		solve();
		out.flush();
		if (!onlineJudge) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) throws Exception {
		new Main().run();
	}

	class InputReader {
		InputStream is;

		public InputReader(boolean onlineJudge) {
			is = onlineJudge ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		String next() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		char[] next(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		char[][] nextMatrix(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		int[] nextArray(int n, boolean isOneInd) {
			int k = isOneInd ? 1 : 0;
			int[] a = new int[n + k];
			for (int i = k; i < n + k; i++)
				a[i] = nextInt();
			return a;
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}
	}
}