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().split())
s=list(input())
l=list("ABCDEFGHIJKLMNOPQRSTUVWXYZ")[:k]
ll=set(l)
if k>=3:
  cnt=0
  for i in range(1,n):
    if s[i]==s[i-1]:
      cnt+=1
      if i+1<n:
        s[i]=list(ll-{s[i-1]}-{s[i+1]})[0]
      else:
        s[i]=list(ll-{s[i-1]})[0]
  print(cnt)
  print("".join(s))
else:
  x=("AB"*n)[:n]
  y=("BA"*n)[:n]
  cnt1,cnt2=0,0
  for i in range(n):
    if x[i]!=s[i]:
      cnt1+=1
    if y[i]!=s[i]:
      cnt2+=1
  if cnt1>=cnt2:
    print(cnt2)
    print(y)
  else:
    print(cnt1)
    print(x)