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:
#!/usr/env python3
from sys import stdin

n, k = map(int, stdin.readline().split())
s = stdin.readline().strip()

cand = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
cnt = 0
if k==2:
    cmps = ("AB"*((n+1)//2))[:n]
    for i in range(n):
        if s[i]!=cmps[i]:
            cnt += 1
    if cnt<n-cnt:
        print(cnt)
        print(cmps)
    else:
        print(n - cnt)
        print(''.join(("BA"*((n+1)//2))[:n]))
else:
    l = 0
    r = 1
    rs = list(s)
    pch = rs[0]
    for i in range(1,n):
        if rs[i]==pch:
            r += 1
        else:
            d = r - l
            if d>1:
                if d%2:
                    l += 1
                for j in range(l,r,2):
                    p = 0
                    while p<k and ((j>0 and rs[j-1]==cand[p]) or (j<n-1 and rs[j+1]==cand[p])):
                        p += 1
                    rs[j] = cand[p]
                    cnt += 1
            pch = rs[i]
            l = r
            r = l+1
    d = r - l
    if d>1:
        if d%2:
            l += 1
        for j in range(l,r,2):
            p = 0
            while p<k and ((j>0 and rs[j-1]==cand[p]) or (j<n-1 and rs[j+1]==cand[p])):
                p += 1
            rs[j] = cand[p]
            cnt += 1
    print(cnt)
    print(''.join(rs))