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 color_stripe(k, road):
    road = list(road)
    if k > 2:
        colors = set('ABC')
        min_cost = 0
        for i in range(1, len(road)):
            if road[i] == road[i - 1]:
                min_cost += 1
                road[i] = list(colors - set(road[i:i+2]))[0]
        return min_cost, ''.join(road)
    else:
        a, b = 'AB' * ((len(road) + 1) / 2), 'BA' * ((len(road) + 1) / 2)
        def cost(r):
            return sum([r[i] != road[i] for i in range(len(road))])
        costa, costb = cost(a), cost(b)
        return min(costa, costb), a[:len(road)] if costa <= costb else b[:len(road)]

def test():
    n, k = map(int, raw_input().split())
    road = raw_input()
    min_cost, new_road = color_stripe(k, road)
    print min_cost
    print new_road

test()