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())

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

if k == 2:
    t = raw_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(raw_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))