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 = input()

if k == 2:
    x = "A"
    y = "B"
    for i in range(1, n):
        if x[-1] == "A":
            x += "B"
        else:
            x += "A"
        if y[-1] == "A":
            y += "B"
        else:
            y += "A"
    p1 = 0
    p2 = 0
    for i in range(n):
        if x[i] != s[i]:
            p1 += 1
        if y[i] != s[i]:
            p2 += 1
    if p1 >= p2:
        print(p2)
        print(y)
    else:
        print(p1)
        print(x)
    exit()
ans = s[0]
colors = []
pts = 0
for i in range(k):
    colors.append(chr(i + 65))
for i in range(1, n):
    x = s[i]
    if x != ans[-1]:
        ans += x
    elif k == 2 or i == n - 1:
        for y in colors:
            if y != x:
                ans += y
                pts += 1
                break
    else:
        z = s[i + 1]
        for y in colors:
            if y != x and y != z:
                ans += y
                pts += 1
                break
print(pts)
print(ans)