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=list(map(int,input().split()))
a=[i for i in input()]
b=0
if k==2:
    for i in range(n):
        if a[i]!='AB'[i%2]:
            b+=1
    if b<n-b:
        print(b)
        print('AB'*(n//2)+'A'*(n%2))
    else:
        print(n-b)
        print('BA'*(n//2)+'B'*(n%2))
else:
    for i in range(1,n):
        if a[i]==a[i-1]:
            for j in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'[:k]:
                if j!=a[i-1] and (i==n-1 or j!=a[i+1]):
                    a[i]=j
                    b+=1
                    break
    print(b)
    print(''.join(a))