Buggy python submission (verdict: Time Limit Exceeded):
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    print(count_changes(s, k)[0])


Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)

Buggy python submission (verdict: Runtime Error):
import string


def count_changes(s, k, pool, prev=None):
    if k == 0:
        return 0, None, None
    t = s * k
    count = 0
    i = 0
    for cur in t:
        if cur == prev:
            count += 1
            prev = pool[i]
            i = (i + 1) % length
        else:
            prev = cur
    return count, i, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    s_set = set(s)
    if len(s) == len(s_set):
        return 0
    pool = list(set(string.ascii_lowercase) - s_set)
    length = len(pool)
    if k <= 2:
        print(count_changes(s, k, pool)[0])
    else:
        base_count, i, prev = count_changes(s, 3, pool)
        d, rest = divmod(k, 3)
        print(base_count * d + count_changes(s, rest, pool, prev)[0])

Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)

Buggy python submission (verdict: Runtime Error):
import string


def count_changes(s, k, pool, prev=None):
    if k == 0:
        return 0, None, None
    t = s * k
    count = 0
    i = 0
    for cur in t:
        if cur == prev:
            count += 1
            prev = pool[i]
            i = (i + 1) % length
        else:
            prev = cur
    return count, i, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    pool = list(set(string.ascii_lowercase) - set(s))
    length = len(pool)
    print(count_changes(s, k, pool)[0])

Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)

Buggy python submission (verdict: Runtime Error):
import string


def count_changes(s, k, pool, prev=None):
    if k == 0:
        return 0, None, None
    t = s * k
    count = 0
    i = 0
    prev = prev or t[0]
    for cur in t[1:]:
        if cur == prev:
            count += 1
            prev = pool[i]
            i = (i + 1) % length
        else:
            prev = cur
    return count, i, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    pool = list(set(string.ascii_lowercase) - set(s))
    length = len(pool)
    if k <= 2:
        print(count_changes(s, k, pool)[0])
    else:
        base_count, i, prev = count_changes(s, 3, pool)
        d, rest = divmod(k, 3)
        print(base_count * d + count_changes(s, rest, pool, i, prev)[0])

Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)

Buggy python submission (verdict: Runtime Error):
import string


def count_changes(s, k, pool, i=0, prev=None):
    if k == 0:
        return 0
    t = s * k
    count = 0
    prev = prev or t[0]
    for cur in t[1:]:
        if cur == prev:
            count += 1
            prev = pool[i]
            i = (i + 1) % length
        else:
            prev = cur
    return count, i, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    pool = list(set(string.ascii_lowercase) - set(s))
    length = len(pool)
    if k <= 2:
        print(count_changes(s, k, pool)[0])
    else:
        base_count, i, prev = count_changes(s, 3, pool)
        d, rest = divmod(k, 3)
        print(base_count * d + count_changes(s, rest, pool, i, prev)[0])

Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)

Buggy python submission (verdict: Runtime Error):
import string


def count_changes(s, k, pool, i=0, prev=None):
    if k == 0:
        return 0
    t = s * k
    count = 0
    prev = prev or t[0]
    for cur in t[1:]:
        if cur == prev:
            count += 1
            prev = pool[i]
            i = (i + 1) % length
        else:
            prev = cur
    return count, i, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    pool = list(set(string.ascii_lowercase) - set(s))
    length = len(pool)
    if k <= 2:
        print(count_changes(s, k, pool)[0])
    else:
        base_count, i, prev = count_changes(s, 3, pool)
        d, rest = divmod(k, 3)
        print(base_count * d + count_changes(s, rest, pool, i, prev))

Fixed submission:
def count_changes(s, k, prev=None):
    count = 0
    for _ in range(k):
        for cur in s:
            if cur == prev:
                count += 1
                prev = None
            else:
                prev = cur
    return count, prev


if __name__ == '__main__':
    s = input()
    k = int(input())
    if len(set(s)) == 1:
      print((len(s) * k) // 2)
      exit()
    if k <= 10 ** 8:
        print(count_changes(s, k)[0])
    else:
        base_count, prev = count_changes(s, 3)
        d, rest = divmod(k, 3)
        res = base_count * d
        if rest:
            res += count_changes(s, rest, prev)[0]
        elif s[0] == prev:
            res += (d - 1)
        print(res)