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 PYTHON3):

Solution:
n,k=map(int,input().split())
s=input()
l=[chr(65+i)for i in range(k)]
p=0
if k==2:
    q="AB"*(n//2)+"A"*(n%2)
    w="BA"*(n//2)+"B"*(n%2)
    o=0
    for i in range(n):
        if s[i]!=q[i]:p+=1
        if s[i]!=w[i]:o+=1
    if p>o:print(o,"\n",w)
    else:print(p,"\n",q)
else:
    s=list(s+"0")
    for i in range(1,n):
        if s[i]==s[i-1]:
            k=s[i]
            for j in l:
                if s[i-1]!=j and s[i+1]!=j:s[i]=j;p+=1;break
    print(p,"\n","".join(s[:-1]))