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=list(raw_input())
if k>2:
    x=set('ABC')
    ans=0
    for i in range(1,n):
        if s[i]==s[i-1]:
            ans+=1
            s[i]=list(x-set(s[i:i+2]))[0]
    print ans
    print ''.join(s)
else:
    ans1,ans2=0,0
    s1='AB'*n
    s2='BA'*n
    for i in range(n):
        if s1[i]!=s[i]:
            ans1+=1
        else:
            ans2+=1
    if ans1<ans2:
        print ans1
        print ''.join(s1[:n])
    else:
        print ans2
        print ''.join(s2[:n])