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())
a=list(input().rstrip())
if k>2:
    ans,s=0,"ABCDEFGHIJKLMNOPQRSTUVWXYZ"[:k]
    for i in range(n-1):
        if a[i]==a[i+1]:
            for j in s:
                if j!=a[i] and (i+2<n and j!=a[i+2] or i==n-2):
                    a[i+1]=j
                    ans+=1
                    break
    print(ans)
    print("".join(a))
else:
    s1,s2,x,y="AB"*(n//2)+"A"*(n%2),"BA"*(n//2)+"B"*(n%2),0,0
    for i in range(n):
        if a[i]!=s1[i]:
            x+=1
        if a[i]!=s2[i]:
            y+=1
    if x>y:
        print(y)
        print(s2)
    else:
        print(x)
        print(s1)