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()

a = []
for i in range(26): a.append(chr(65 + i))

def diff(x, y):
    c = 0
    for i in range(len(x)):
        if x[i] != y[i]: c+= 1
    return c

if k == 2:
    ta = ('AB' * (n / 2 + 1))[:n]
    tb = ('BA' * (n / 2 + 1))[:n]
    ma = diff(ta, s)
    mb = diff(tb, s)
    if ma < mb:
        m = ma
        t = ta
    else:
        m = mb
        t = tb
    print m
    print t
else:
    m = 0
    t = s[0]
    for i in range(1, n):
        if s[i] == t[i - 1]:
            for x in a:
                if x != t[i - 1] and (x != s[i + 1] if i + 1 < n else True):
                    t += x
                    break
            m += 1
        else: t += s[i]

    print m
    print t