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:
def sol(p, s):
    n, k = map(int, p)
    if n==1:
        p = 0, s
    elif k==2:
        ab,ba = [sum(1 for i,v in enumerate(s) if v!=t[i&1]) for t in 'AB','BA']
        p = ab<ba and (ab, n/2*'AB' + n%2*'A') or (ba, n/2*'BA' + n%2*'B')
    else:
        a, i, s, p = 0, 1, bytearray(s), {65, 66, 67}
        while i<n:
            if s[i]==s[i-1]:
                s[i] = (p - set(s[i:i+2])).pop(); i += 2; a += 1
            else:
                i += 1
        p = a, s
    return p

r = raw_input
for i in sol(r().split(), r()): print i