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:
from sys import stdin

rstr = lambda: stdin.readline().strip()
rints = lambda: [int(x) for x in stdin.readline().split()]

n, k = rints()
s, ans = list(rstr()), 0

if k > 2:
    for i in range(1, n):
        if s[i] == s[i - 1]:
            ans += 1
            for j in range(ord('A'), ord('A') + k):
                ch = chr(j)
                if ch != s[i - 1]:
                    if i == n - 1 or ch != s[i + 1]:
                        s[i] = ch
                        break
    s = ''.join(s)
else:
    tem = [0, 0]
    for i in range(n):
        if s[i] == 'A':
            if i % 2:
                tem[0] += 1
            else:
                tem[1] += 1

        else:
            if i % 2:
                tem[1] += 1
            else:
                tem[0] += 1

    if tem[0] <= tem[1]:
        ans = tem[0]
        s = 'AB' * (n // 2) + 'A' * (n % 2)
    else:
        ans = tem[1]
        s = 'BA' * (n // 2) + 'B' * (n % 2)

print(ans)
print(s)