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.*;
import java.math.*;

public class C {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		String s = sc.next();
		
		if(k == 2){
			int first = 0;
			int second = 0;
			
			for(int i=0; i<n; i+=2){
				if(s.charAt(i) == 'B'){
					first++;
				}else{
					second++;
				}
			}
			
			for(int i=1; i<n; i+=2){
				if(s.charAt(i) == 'A'){
					first++;
				}else{
					second++;
				}
			}
			
			if(first < second){
				System.out.println(first);
				StringBuilder sb = new StringBuilder();
				
				while(true){
					sb.append("A");
					if(sb.length() == n){
						break;
					}
					sb.append("B");
					if(sb.length() == n){
						break;
					}
				}
				
				System.out.println(sb);
			}else{
				System.out.println(second);
				StringBuilder sb = new StringBuilder();
				
				while(true){
					sb.append("B");
					if(sb.length() == n){
						break;
					}
					sb.append("A");
					if(sb.length() == n){
						break;
					}
				}
				
				System.out.println(sb);
			}
		}else{
			StringBuilder sb = new StringBuilder();
			
			int limit = s.length()-2;
			int change = 0;
			
			for(int i=0; i<limit; i++){
				sb.append(s.charAt(i));
				
				if(s.charAt(i) == s.charAt(i+1)){
					char c = s.charAt(i+2);
					
					if(s.charAt(i) != 'A' && c != 'A'){
						sb.append('A');
					}else if(s.charAt(i) != 'B' && c != 'B'){
						sb.append('B');
					}else{
						sb.append('C');
					}
					
					i++;
					change++;
				}
			}
			
			if(sb.length() == limit){
				if(s.charAt(limit) == s.charAt(limit+1)){
					sb.append(s.charAt(limit));
					
					if(s.charAt(limit) != 'A'){
						sb.append('A');
					}else{
						sb.append('B');
					}
					
					change++;
				}else{
					sb.append(s.charAt(limit));
					sb.append(s.charAt(limit+1));
				}
			}else{
				sb.append(s.charAt(limit+1));
			}
			
			System.out.println(change);
			System.out.println(sb);
		}
	}
}