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 = [i for i in input()]
d = {i:chr(65+i) for i in range(k)}
ct = 0

if k == 2:
    a1 = []
    a2 = []
    
    for i in range(n):
        a1.append(d[i%2])
        a2.append(d[(1+i)%2])
        
    ct1 = 0
    ct2 = 0
    
    for i in range(n):
        if s[i] != a1[i]:
            ct1 += 1
        if s[i] != a2[i]:
            ct2 += 1
            
    if ct2 < ct1:
        print(ct2)
        print("".join(a2))
    else:
        print(ct1)
        print("".join(a1))
    
else:
    for i in range(1, n):
        if s[i] == s[i-1]:
            s[i] = " "
            ct += 1

    for i in range(1, n-1):
        if s[i] == " ":
            for j in range(k):
                if s[i-1] != d[j] and s[i+1] != d[j]:
                    s[i] = d[j]
                    break

    if s[-1] == " ":
        for j in range(k):
            if s[-2] != d[j]:
                s[-1] = d[j]
                break

    print(ct)
    print("".join(s))