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:
n, k = map(int, raw_input().split(' '))
s = raw_input()

if k == 2:
    diff1 = 0
    diff2 = 0
    s1 = ''
    s2 = ''
    for i in range(n):
        s1 += chr(ord('A') + (i % 2))
        s2 += chr(ord('B') - (i % 2))
        if s[i] == chr(ord('A') + (i % 2)):
            diff2 += 1
        else:
            diff1 += 1
    if diff1 < diff2:
        print diff1
        print s1
    else:
        print diff2
        print s2
else:
    res = []
    prefix = ''
    idx = 0
    changes = 0
    while idx < len(s):
        if idx + 1 == len(s) or s[idx] != s[idx + 1]:
            prefix += s[idx]
            res.append(prefix[0])
            col = 'A' if prefix[0] != 'A' else 'B'
            col2 = 'C' if prefix[0] != 'C' else 'B'
            if len(prefix) % 2 == 1:
                for i in range(1, len(prefix)):
                    res.append(col if (i % 2 == 1) else prefix[0])
                    if i % 2 == 1:
                        changes += 1
            else:
                if len(prefix) > 2:
                    for i in range(1, len(prefix) - 1):
                        if i % 2 == 1:
                            res.append(col)
                            changes += 1
                        else:
                            res.append(prefix[0])
                    res[-1] = col2
                    changes += 1
                    res.append(prefix[-1])
                else: # prefix = XX
                    if idx + 1 == len(s):
                        res.append(col)
                    else:
                        res.append(col if col != s[idx + 1] else col2)
                    changes += 1
            prefix = ''
            idx += 1
        else:
            prefix += s[idx]
            idx += 1
    print changes
    print ''.join(res)