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:
n,k=map(int,raw_input().split())
s=list(str(raw_input()))
i=1
c=0
s.append(-1)
if k==2:
    t1='AB'*(n/2)+'A'*(n%2)
    t2='BA'*(n/2)+'B'*(n%2)
    c1=0
    c2=0
    for i in range(0,n):
        if s[i]!=t1[i]:
            c1=c1+1
        if s[i]!=t2[i]:
            c2=c2+1
    if c1>c2:
        print c2
        print t2
    else:
        print c1
        print t1
    exit()

while i<len(s):

    if s[i]==s[i-1]:
        if s[i-1]!='A'and s[i+1]!='A':
            s[i]='A'
        elif s[i-1]!='B'and s[i+1]!='B':
            s[i]='B'
        else:
            s[i]='C'

        c=c+1
        i=i+2
    else:
        i=i+1
s2=""
for i in range(0,n):
    s2=s2+s[i]
print c
print s2