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 math
import sys
from bisect import bisect_right, bisect_left, insort_right
from collections import Counter, defaultdict
from heapq import heappop, heappush
from itertools import accumulate, permutations
from sys import stdout

R = lambda: map(int, input().split())
n, k = R()
s = input()
cnt = 0
if k == 2:
    s1, s2 = ('AB' * ((n + 1) // 2))[:n], ('BA' * ((n + 1) // 2))[:n]
    cnt1 = cnt2 = 0
    for i in range(n):
        cnt1 += s[i] != s1[i]
        cnt2 += s[i] != s2[i]
    if cnt1 < cnt2:
        s = s1
        cnt = cnt1
    else:
        s = s2
        cnt = cnt2
else:
    s = list(s)
    for i in range(1, n):
        if s[i] == s[i - 1]:
            for j in range(k):
                c = chr(ord('A') + j)
                if c != s[i - 1] and (i == n - 1 or c != s[i + 1]):
                    s[i] = c
            cnt += 1
print(cnt)
print(''.join(s))