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 string
n,k=map(int,input().split())
r=list(input())
if k==2:
    t='AB'*(n//2)+'A'*(n%2)
    p='BA'*(n//2)+'B'*(n%2)
    ct=0;cp=0
    for i in range(n):
        if r[i]!=t[i]:
            ct+=1
        if r[i]!=p[i]:
            cp+=1
    if cp<ct:
        print(cp)
        print(''.join(p))
    else:
        print(ct)
        print(''.join(t))
else:
    ans=0
    for i in range(1,n):
        c=list(string.ascii_uppercase)[:k]
        if r[i]==r[i-1]:
            c.remove(r[i])
            if i+1<n and r[i+1] in c:
                c.remove(r[i+1])
            if len(c)>0:
                r[i]=c.pop()
            else:
                c = list(string.ascii_uppercase)[:k]
                if r[i] == r[i - 1]:
                    c.remove(r[i])
                    if 0 <= i - 2 < n and r[i - 1] in c:
                        c.remove(r[i - 2])
                    r[i-1] = c.pop()
            ans+=1
    print(ans)
    print(''.join(r))