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:
import sys
input=sys.stdin.readline
n,k=map(int,input().split())
s=list(input().rstrip())
al=list("abcdefghijklmnopqrstuvwxyz".upper())[:k]
al=set(al)
if k>=3:
    cnt=0
    for i in range(1,n-1):
        if s[i-1]==s[i]==s[i+1]:
            s[i]=list(al-{s[i-1]})[0]
            cnt+=1
    for i in range(1,n):
        if s[i]==s[i-1]:
            if i<n-1:
                s[i]=list(al-{s[i-1]}-{s[i+1]})[0]
            else:
                s[i]=list(al-{s[i-1]})[0]
            cnt+=1
    print(cnt)
    print("".join(s))
else:
    s1="AB"*(n//2)+"A"*(n%2)
    s2="BA"*(n//2)+"B"*(n%2)
    cnt1,cnt2=0,0
    for i in range(n):
        if s[i]!=s1[i]:
            cnt1+=1
        if s[i]!=s2[i]:
            cnt2+=1
    if cnt1<cnt2:
        print(cnt1)
        print(s1)
    else:
        print(cnt2)
        print(s2)