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:
'''
Sun Oct 19 01:45:01 PDT 2014
135 Div2 prob c
Greedy / Implentation
'''
nums = map(int, raw_input('').split(' '))
n = nums[0]
k = nums[1]
pattern = raw_input('')


def first(ch, ch2):
    start = ord('A')
    while start <= ord('Z'):
        if chr(start) != ch and chr(start) != ch2:
            return chr(start)
        start += 1


def cnt(patternt, ans):
    count = 0
    for i in xrange(len(patternt)):
        if patternt[i] != ans[i]:
            count += 1
    return count

if k >= 3:
    seqs = []
    cur = 1
    count = 1
    seqs.append([pattern[0], 1])
    while cur < len(pattern):
        if pattern[cur] == pattern[(cur - 1)]:
            seqs[count - 1][1] += 1
        else:
            seqs.append([pattern[cur], 1])
            count += 1
        cur += 1
    num_repaint = 0
    ans = ''
    cur = 0
    for c in seqs:
        num_repaint += (c[1] / 2)
        for i in xrange(c[1]):
            if i % 2 == 1:
                if cur + 1 < len(seqs):
                    ans += first(c[0], seqs[cur + 1][0])
                else:
                    ans += first(c[0], c[0])
            else:
                ans += c[0]
        cur += 1
    print num_repaint
    print ans
else:
    '''
    for k == 2 there are only 2 seqs possible.
        ABABAB...
          OR
        BABABA
    '''
    ans1 = 'AB' * (n / 2) + ('A' if n % 2 == 1 else '')
    ans2 = 'BA' * (n / 2) + ('B' if n % 2 == 1 else '')
    count1 = cnt(pattern, ans1)
    count2 = cnt(pattern, ans2)
    if count1 <= count2:
        print count1
        print ans1
    if count1 > count2:
        print count2
        print ans2