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())

s = list(input())

if k > 2:
    c = set(ord("A") + i for i in range(26))
    r = 0
    for i in range(1,len(s)):
        if s[i-1] == s[i]:
            r += 1
            if i + 1 < n:
                s[i] = "A" if "A" not in {s[i-1], s[i+1]} else ('B' if "B" not in {s[i], s[i+1]} else "C")
            else:
                s[i] = "A" if s[i-1] != "A" else "B"
    
    print(r)
    print("".join(s))

else:
    x, y = "AB" * n, "BA" * n
    def check(x, y):
        return sum(x[i] != y[i] for i in range(n))
    check_1 = check(x, s)
    check_2 = check(y, s)
    z = [x,y][check_1 > check_2]
    print(min(check_1, check_2))
    print(z[:n])