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 diff(a,b):
    return sum([1 for x in xrange(len(a)) if a[x]!=b[x]])
n,k = map(int,raw_input().split())
s = list(raw_input()) + ['']
if k == 2:
    a ='AB'*(n/2)+'A'*(n%2)
    b ='BA'*(n/2)+'B'*(n%2)
    print min(diff(a,s),diff(b,s))
    print [a,b][diff(b,s) <= diff(a,s)]
else:
    c,p = set('ABC'),0
    for i in xrange(1,n):
        if s[i-1] == s[i]:
            p += 1
            s[i] = list(c-set(s[i:i+2]))[0]
    print p
    print ''.join(s)