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:
def main():
    n, k = map(int, raw_input().split())
    s = [ch for ch in raw_input()]
    letters = [chr(ord('A') + i) for i in xrange(k)]

    if k == 2:
        a, b = 0, 0
        for i, ch in enumerate(s):
            if ch == ['A', 'B'][i % 2]:
                a += 1
            else:
                b += 1
        res = ''
        if a > b:
            for i in xrange(len(s)):
                res += ['A', 'B'][i % 2]
            print n - a
        else:
            for i in xrange(len(s)):
                res += ['B', 'A'][i % 2]
            print n - b
        print res
        return

    count, pos = 0, 1

    while pos < n:
        if s[pos] == s[pos - 1]:
            count += 1
            try:
                s[pos] = (ch for ch in letters if ch != s[pos] and
                    (pos == n - 1 or ch != s[pos + 1])).next()
            except StopIteration:
                s[pos] = s[pos + 1]
        pos += 1
    print count
    print ''.join(s)

if __name__ == '__main__':
    main()