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:
import itertools

n, k = map(int, input().split())
if k == 2:
    ab, ba = "AB" * (n // 2) + "A" * (n % 2), "BA" * (n // 2) + "B" * (n % 2)
    ab_c, ba_c = 0, 0
    old = input().strip()
    for i in range(n):
        if old[i] != ab[i]:
            ab_c += 1
        if old[i] != ba[i]:
            ba_c += 1
    if ab_c < ba_c:
        print(ab_c)
        print(ab)
    else:
        print(ba_c)
        print(ba)
else:
    old, req, avail = [char for char in input().strip()], 0, "ABCDEFGHIJKLMNOPQRSTUVWXYZA"
    for i in range(1, n):
        if old[i] == old[i - 1]:
            old[i] = avail[(avail.find(old[i - 1]) + 1) % k]
            if i != n - 1 and old[i] == old[i + 1]:
                old[i] = avail[(avail.find(old[i]) + 1) % k]
            req += 1
    print(req)
    print("".join(old))