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().strip().split())
s = list(input())
options = [chr(ord('A')+i) for i in range(k)]
ans = 0

if k == 2:
    ans1 = ['A' if i%2 == 0 else 'B' for i in range(n)]
    diff1 = 0
    for i in range(n):
        if s[i] != ans1[i]:
            diff1 += 1
    if diff1 < n-diff1:
        print(diff1)
        print(''.join(ans1))
    else:
        print(n-diff1)
        print('B' + ''.join(ans1[:-1]))
else:
    for i in range(1, n-1):
        if s[i] == s[i-1]:
            ans += 1
            for j in options:
                if j != s[i-1] and j != s[i+1]:
                    s[i] = j
                    break
            
    if n > 1 and s[-2] == s[-1]:
        ans += 1
        s[-1] = options[0] if options[0] != s[-2] else options[1]
    print(ans)
    print(''.join(s))