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:
import string

n, k = map(int, raw_input().split(' '))
s = raw_input()

letters = string.uppercase[:k]

ans = 0

if k == 2:
    s1 = 'AB' * (len(s) / 2) + ('A' if len(s) % 2 != 0 else '')
    s2 = 'BA' * (len(s) / 2) + ('B' if len(s) % 2 != 0 else '')
    ans1, ans2 = 0, 0
    for i in xrange(n):
        if s[i] != s1[i]:
            ans1 += 1
        if s[i] != s2[i]:
            ans2 += 1
    if ans1 < ans2:
        ans = ans1
        s = s1
    else:
        ans = ans2
        s = s2
else:
    s = list(s)
    for i in xrange(1, n):
        if s[i] == s[i - 1]:
            for c in letters:
                if c != s[i] and (i + 1 == n or c != s[i + 1]):
                    s[i] = c
                    break
            ans += 1
    s = ''.join(s)
        
print ans
print s