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())
r=list(raw_input())
if k==2:
    s='AB'*n
    m=lambda x,y:sum(x[i] != y[i] for i in range(n))
    if m(s[1:n+1],r) < m(s[:n],r):
        print m(s[1:n+1],r)
        print s[1:n+1]
    else:
        print m(s[:n],r)
        print s[:n]
    exit()
c=0
s=set(map(lambda x:chr(x+ord('A')), range(k)))
for i in range(1,n):
    if r[i-1] == r[i]:
        c+=1
        r[i]=list(s-set([r[i-1]] +([] if i==n-1 else [r[i+1]])))[0]
print  c
print ''.join(r)