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:
from itertools import *
n,k=map(int,raw_input().split())
s=raw_input()
if k==2:
    xx="AB"
    fsts="AB"*n
    scds="BA"*n
    fst,scd=0,0
    for c1,c2,c3 in izip(s,fsts,scds):
        if c1!=c2:
            fst+=1
        if c1!=c3:
            scd+=1            
    if fst<scd:
        print fst
        print fsts[:n]
    else:
        print scd
        print scds[:n]
elif n==1:
    print 0
    print s
else:    
    pred='?'
    aa=[c for c in s]
    res=0
    for i in xrange(1,n-1):   
         if aa[i]==aa[i-1]:
            res+=1
            if (aa[i-1]!='A')and(aa[i+1]!='A'):
                aa[i]='A'
            if (aa[i-1]!='B')and(aa[i+1]!='B'):
                aa[i]='B'
            if (aa[i-1]!='C')and(aa[i+1]!='C'):
                aa[i]='C'
    if aa[n-1]==aa[n-2]:
        res+=1
        if aa[n-2]!='A':
            aa[n-1]='A'
        if aa[n-2]!='B':
            aa[n-1]='B'
    print res        
    print "".join(aa)