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 PYTHON):

Solution:
def find(a,b,col):
    s=''
    for i in range(len(col)):
        if(col[i]!=a and col[i]!=b):
            s=col[i]
            break
    return s
n,k=map(int,raw_input().strip().split(" "))
col=[]
for i in range(k):
    col.append(chr(i+65))
s=raw_input()
s1,s2,tot1,tot2='','',0,0
if(k==2):
    for i in range(n):
        if(i%2==0):
            s1+='A'
            s2+='B'
        else:
            s1+='B'
            s2+='A'
        if(s1[i]!=s[i]):
            tot1+=1
        if(s2[i]!=s[i]):
            tot2+=1
    if(tot1<=tot2):
        print tot1
        print s1
    else:
        print tot2
        print s2
else:
    s1=s1+s[0]
    for i in range(n-1):
        if(s1[i]==s[i+1] and (i+2)!=n):
            c=find(s1[i],s[i+2],col)
            s1+=c
            tot1+=1
        elif(s1[i]==s[i+1] and (i+2)==n):
            num=ord(s[i+1])-65
            c=col[(num+1)%k]
            s1=s1+c
            tot1+=1
        else:
            s1=s1+s[i+1]
    print tot1
    print s1