Buggy python submission (verdict: Runtime Error):
# Author: cr4zjh0bp
# Created: Sat Mar 14 20:41:10 UTC 2020
import sys
 
stdin = sys.stdin
inf = 1 << 60
mod = 1000000007
 
ni = lambda: int(ns())
nin = lambda y: [ni() for _ in range(y)]
na = lambda: list(map(int, stdin.readline().split()))
nan = lambda y: [na() for _ in range(y)]
nf = lambda: float(ns())
nfn = lambda y: [nf() for _ in range(y)]
nfa = lambda: list(map(float, stdin.readline().split()))
nfan = lambda y: [nfa() for _ in range(y)]
ns = lambda: stdin.readline().rstrip()
nsn = lambda y: [ns() for _ in range(y)]
ncl = lambda y: [list(ns()) for _ in range(y)]
nas = lambda: stdin.readline().split()

from collections import Counter

s = ns()
n = len(s)
s = s + "$"
k = ni()

c = []
cnt = 1
for i in range(len(s) - 1):
    if s[i] == s[i + 1]:
        cnt += 1
    elif cnt > 1:
        c.append(cnt)
        cnt = 1

if len(c) == 1 and c[0] == n:
    print(n * k // 2)
elif s[0] != s[-2]:
    print(sum([x // 2 for x in c[:]]) * k)
else:
    a, b = 1, 1
    if s[0] == s[1]:
        a = c[0]
    if s[-2] == s[-3]:
        b = c[-1]
    print(sum([x // 2 for x in c[:]]) * k - (a // 2 + b // 2 - (a + b) // 2) * (k - 1))

Fixed submission:
# Author: cr4zjh0bp
# Created: Sat Mar 14 20:41:10 UTC 2020
import sys
 
stdin = sys.stdin
inf = 1 << 60
mod = 1000000007
 
ni = lambda: int(ns())
nin = lambda y: [ni() for _ in range(y)]
na = lambda: list(map(int, stdin.readline().split()))
nan = lambda y: [na() for _ in range(y)]
nf = lambda: float(ns())
nfn = lambda y: [nf() for _ in range(y)]
nfa = lambda: list(map(float, stdin.readline().split()))
nfan = lambda y: [nfa() for _ in range(y)]
ns = lambda: stdin.readline().rstrip()
nsn = lambda y: [ns() for _ in range(y)]
ncl = lambda y: [list(ns()) for _ in range(y)]
nas = lambda: stdin.readline().split()

from collections import Counter

s = ns()
n = len(s)
s = s + "$"
k = ni()

c = []
cnt = 1
for i in range(len(s) - 1):
    if s[i] == s[i + 1]:
        cnt += 1
    elif cnt > 1:
        c.append(cnt)
        cnt = 1

if (len(c) == 1 and c[0] == n) or n == 1:
    print(n * k // 2)
elif s[0] != s[-2]:
    print(sum([x // 2 for x in c[:]]) * k)
else:
    a, b = 1, 1
    if s[0] == s[1]:
        a = c[0]
    if s[-2] == s[-3]:
        b = c[-1]
    print(sum([x // 2 for x in c[:]]) * k - (a // 2 + b // 2 - (a + b) // 2) * (k - 1))

Buggy python submission (verdict: Runtime Error):
# Author: cr4zjh0bp
# Created: Sat Mar 14 19:55:57 UTC 2020
import sys
 
stdin = sys.stdin
inf = 1 << 60
mod = 1000000007
 
ni = lambda: int(ns())
nin = lambda y: [ni() for _ in range(y)]
na = lambda: list(map(int, stdin.readline().split()))
nan = lambda y: [na() for _ in range(y)]
nf = lambda: float(ns())
nfn = lambda y: [nf() for _ in range(y)]
nfa = lambda: list(map(float, stdin.readline().split()))
nfan = lambda y: [nfa() for _ in range(y)]
ns = lambda: stdin.readline().rstrip()
nsn = lambda y: [ns() for _ in range(y)]
ncl = lambda y: [list(ns()) for _ in range(y)]
nas = lambda: stdin.readline().split()

s = ns()
k = ni()

c = []
cnt = 1
for i in range(len(s) - 1):
    if s[i] == s[i + 1]:
        cnt += 1
    elif cnt > 1:
        c.append(cnt)
        cnt = 1
if cnt > 1:
    c.append(cnt)

itv = 0
if len(s) > 1 and len(c) > 0:
    if s[0] == s[1] and s[-1] == s[-2]:
        itv = sum([x // 2 for x in c[1:-1]])
    elif s[0] == s[1] and s[-1] != s[-2]:
        itv = sum([x // 2 for x in c[1:]])
    elif s[0] != s[1] and s[-1] == s[-2]:
        itv = sum([x // 2 for x in c[:-1]])
    else:
        itv = sum([x // 2 for x in c[:]])

if len(c) == 1 and c[0] == len(s):
    # 全ての要素が連続している
    print(len(s) * k // 2)
elif s[0] != s[-1]:
    # 両端が連続していない
    print(itv * k)
else:
    ans = 0
    # 左端を操作する必要がある
    if s[0] == s[1]:
        ans += c[0] // 2
    # 右端を操作する必要がある
    if s[-1] == s[-2]:
        ans += c[-1] // 2

    # 左端、右端以外
    ans += itv * k

    if len(c) == 0:
        # 左端と右端がどちらも連続していない
        ans += k - 1
    else:
        if s[0] == s[1] and s[-1] == s[-2]:
            # 両端に連続した要素がある
            ans += (c[-1] + c[0]) // 2 * (k - 1)
        elif s[0] == s[1] and s[-1] != s[-2]:
            # 右端に連続した要素がない
            ans += (c[1] + 1) // 2 * (k - 1)
        else:
            # 左端に連続した要素がない
            ans += (c[-1] + 1) // 2 * (k - 1)

    print(ans)

Fixed submission:
# Author: cr4zjh0bp
# Created: Sat Mar 14 20:41:10 UTC 2020
import sys
 
stdin = sys.stdin
inf = 1 << 60
mod = 1000000007
 
ni = lambda: int(ns())
nin = lambda y: [ni() for _ in range(y)]
na = lambda: list(map(int, stdin.readline().split()))
nan = lambda y: [na() for _ in range(y)]
nf = lambda: float(ns())
nfn = lambda y: [nf() for _ in range(y)]
nfa = lambda: list(map(float, stdin.readline().split()))
nfan = lambda y: [nfa() for _ in range(y)]
ns = lambda: stdin.readline().rstrip()
nsn = lambda y: [ns() for _ in range(y)]
ncl = lambda y: [list(ns()) for _ in range(y)]
nas = lambda: stdin.readline().split()

from collections import Counter

s = ns()
n = len(s)
s = s + "$"
k = ni()

c = []
cnt = 1
for i in range(len(s) - 1):
    if s[i] == s[i + 1]:
        cnt += 1
    elif cnt > 1:
        c.append(cnt)
        cnt = 1

if (len(c) == 1 and c[0] == n) or n == 1:
    print(n * k // 2)
elif s[0] != s[-2]:
    print(sum([x // 2 for x in c[:]]) * k)
else:
    a, b = 1, 1
    if s[0] == s[1]:
        a = c[0]
    if s[-2] == s[-3]:
        b = c[-1]
    print(sum([x // 2 for x in c[:]]) * k - (a // 2 + b // 2 - (a + b) // 2) * (k - 1))