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 c219 {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		char[] word = in.next().toCharArray();

		int[][] memo = new int[k][n];
		int[][] last = new int[k][n];

		for (int i = 0; i < k; i++) {
			memo[i][0] = word[0] - 'A' == i ? 0 : 1;
		}

		int first = word[0] - 'A';
		int second = first == 0 ? 1 : 0;
		int firstV = 0;
		int secondV = 1;
		for (int i = 1; i < n; i++) {
			int a = 0;
			int b = 0;
			int aV = Integer.MAX_VALUE;
			int bV = Integer.MAX_VALUE;

			for (int hl = 0; hl < k; hl++) {
				memo[hl][i] = Integer.MAX_VALUE;
				int v = (word[i] - 'A' == hl ? 0 : 1)
						+ (hl == first ? secondV : firstV);
				memo[hl][i] = v;
				last[hl][i] = hl == first ? second : first;
				if (v < aV) {
					b = a;
					bV = aV;
					a = hl;
					aV = v;
				} else if (v < bV) {
					b = hl;
					bV = v;
				}
			}

			first = a;
			second = b;
			firstV = aV;
			secondV = bV;
		}

		int bestIdx = 0;
		for (int i = 1; i < k; i++) {
			if (memo[i][n - 1] < memo[bestIdx][n - 1])
				bestIdx = i;
		}
		System.out.println(memo[bestIdx][n - 1]);
		int idx = n;
		while (idx-- > 0) {
			word[idx] = (char) ('A' + bestIdx);
			bestIdx = last[bestIdx][idx];
		}
		System.out.println(word);
	}
}