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:
n, k = map(int, raw_input().split())
s = list(raw_input() + ' ')
if k > 2:
	c, r = set('ABC'), 0
	for i in range(1, n):
		if s[i - 1] == s[i]:
			r += 1
			s[i] = list(c - set([s[i - 1], s[i + 1] if i + 1 < len(s) else '']))[0]
	print r
	print ''.join(s)
else:
	f = lambda x : sum(x[i] != s[i] for i in range(n))
	x, y = 'AB' * n, 'BA' * n
	z = [x, y][f(x) > f(y)]
	print f(z)
	print z[ : n]