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 PYTHON3):

Solution:
n, k = map(int, input().split())



p = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'[: k] + 'A'

p = {p[i] : p[i + 1] for i in range(k)}



if k == 2:

    t = input()

    u, v = 'AB' * (n // 2) + 'A' * (n % 2), 'BA' * (n // 2) + 'B' * (n % 2)

    x, y = sum(int(u[i] != t[i]) for i in range(n)), sum(int(v[i] != t[i]) for i in range(n))

    if x < y:

        print(x)

        print(u)

    else:

        print(y)

        print(v)    

else:

    t, s = list(input()), 0

    for i in range(1, n):

        if t[i] == t[i - 1]:

            t[i] = p[t[i]]

            if i + 1 < n and t[i] == t[i + 1]: t[i] = p[t[i]]

            s += 1

    print(s)

    print(''.join(t))



# Made By Mostafa_Khaled