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 = list(input())

if k <= 2:
    f = lambda t : sum(int(t[i] != s[i]) for i in range(n))
    x, y = 'AB' * n, 'BA' * n
    res_x, res_y = f(x), f(y)
    if res_x > res_y:
        print(res_y)
        print(y[:n])
    else:
        print(res_x)
        print(x[:n])
    exit()

res = 0
for i in range(1, n):
	if s[i-1] == s[i]:
		res += 1
		s[i] = list(set('ABC') - set(s[i:i+2]))[0]
print(res)
print(''.join(s))