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 = raw_input()

i = 1
ln = len(s)

res = []
ct = 0
if k == 2:
    ab = 0
    ba = 0
    s = str(s)
    for i in xrange(0, len(s), 2):
        if s[i] == 'B': ab += 1
        elif s[i] == 'A': ba += 1
        if i+1 < ln: 
            if s[i+1] == 'A': ab += 1
            elif s[i+1] == 'B': ba += 1
    if ab < ba:
        ct = ab
        s = 'AB'*(n/2)+'A'*(n%2)
    else:
        ct = ba
        s = 'BA'*(n/2)+'B'*(n%2)
else:
    s = bytearray(s)
    colors = set(ord('A')+c for c in xrange(k))
    for i in xrange(1, len(s)):
        if s[i] == s[i-1]:
            used = set([s[i-1]])
            if i+1 < ln: used.add(s[i+1])
            s[i] = (colors - used).pop()
            ct += 1

print ct
print s