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())
l=list(raw_input())
if k==2:
    cnt1=0 
    cnt2=0 
    cand1="AB"*(n//2)+"AB"[:n%2]
    cand2="BA"*(n//2)+"BA"[:n%2]
    for i in range(n):
        if l[i]!=cand1[i]: cnt1+=1 
        if l[i]!=cand2[i]: cnt2+=1 
    if cnt1<cnt2:
        print(cnt1)
        print(cand1)
    else:
        print(cnt2)
        print(cand2)
    exit()
cnt=0 
def chk2(ch1,ch2):
    for i in range(k):
        if chr(i+65)!=ch1 and chr(i+65)!=ch2: 
            return chr(i+65)
def chk1(ch1):
    for i in range(k):
        if chr(i+65)!=ch1:
            return chr(i+65)
for i in range(1,n):
    if l[i]==l[i-1]:
        
        if i!=n-1:
            l[i]=chk2(l[i-1],l[i+1])
        else:
            l[i]=chk1(l[i-1])
        cnt+=1 
print(cnt)
print(''.join(l))