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 itertools
import bisect
# import math
from collections import defaultdict
import os
import sys
from io import BytesIO, IOBase

# sys.setrecursionlimit(10 ** 5)
ii = lambda: int(input())
lmii = lambda: list(map(int, input().split()))
slmii = lambda: sorted(map(int, input().split()))
li = lambda: list(input())
mii = lambda: map(int, input().split())
msi = lambda: map(str, input().split())


def gcd(a, b):
    if b == 0: return a
    return gcd(b, a % b)


def lcm(a, b): return (a * b) // gcd(a, b)


def main():
    # for _ in " " * int(input()):
    n, k = mii()
    s = li()
    a = ["A", "B", "C"]
    cnt = 0
    if n == 1:
        print(0)
        print("".join(s))
    elif n == 2:
        if s[0] != s[1]:
            print(0)
            print("".join(s))
        else:
            print(1)
            if s[0] == "A":
                print("AB")
            else:
                print(s[0]+"A")
    else:
        if k > 2:
            for i in range(1, n - 1):
                if s[i] == s[i - 1] and s[i] == s[i + 1]:
                    cnt += 1
                    s[i] = (set(a) - {s[i - 1], s[i + 1]}).pop()
            for i in range(1, n - 1):
                if s[i] == s[i-1] or s[i] == s[i+1]:
                    cnt += 1
                    s[i] = (set(a) - {s[i - 1], s[i + 1]}).pop()
            print(cnt)
            print("".join(s))
        else:
            f = []
            ss = []
            for i in range(n):
                if i % 2 == 0:
                    ss.append("B")
                    f.append("A")
                else:
                    f.append("B")
                    ss.append("A")
            fc = 0
            sc = 0
            for i in range(n):
                if s[i] != f[i]:
                    fc += 1
                else:
                    sc += 1
            if fc < sc:
                print(cnt + fc)
                print("".join(f))
            else:
                print(cnt + sc)
                print("".join(ss))




BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

if __name__ == "__main__":
    main()