Buggy python submission (verdict: Time Limit Exceeded):
n,k = map(int,input().split())
P = [-1] + list(map(int,input().split())) + [10**6]
Q = [''.join(map(str,P))]
for i in range(1,n-k+1):
    if (sorted(P[i-1:i+k-1])[1:k] != sorted(P[i:i+k])[0:k-1] or i==1 or i == n-k+1)and P[i:i+k] != sorted(P[i:i+k]):
        q = P[:i] + sorted(P[i:i+k]) + P[i+k:]
        Q += [''.join(map(str,q))]
print(len(Q))


Fixed submission:
class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, index):
        res = 0
        while index:
            res += self.tree[index]
            index -= index & -index
        return res

    def add(self, index, x):
        while index <= self.n:
            self.tree[index] += x
            index += index & -index

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1


N, K = map(int, input().split())
P = list(map(lambda x: int(x) + 1, input().split()))

bit = BinaryIndexedTree(N + 1)
count = 1

for i in range(K):
    bit.add(P[i], 1)

for i in range(N - K):
    mi = bit.bisect_left(1)
    ma = bit.bisect_left(K)
    if P[i] != mi or P[K + i] < ma:
        count += 1
    bit.add(P[i], -1)
    bit.add(P[K + i], 1)

inc = 1
incseq = 0

for i in range(N - 1):
    if P[i] < P[i + 1]:
        inc += 1
        if inc == K:
            incseq += 1
    else:
        inc = 1

print(count - max(0, incseq - 1))

Buggy python submission (verdict: Time Limit Exceeded):
n,k = map(int,input().split())
P = [-1] + list(map(int,input().split())) + [2*(10**5)+1]
Q = [''.join(map(str,P))]
for i in range(1,n-k+1):
    q = P[:i] + sorted(P[i:i+k]) + P[i+k:]
    Q += [''.join(map(str,q))]
print(len(set(Q)))

Fixed submission:
class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, index):
        res = 0
        while index:
            res += self.tree[index]
            index -= index & -index
        return res

    def add(self, index, x):
        while index <= self.n:
            self.tree[index] += x
            index += index & -index

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1


N, K = map(int, input().split())
P = list(map(lambda x: int(x) + 1, input().split()))

bit = BinaryIndexedTree(N + 1)
count = 1

for i in range(K):
    bit.add(P[i], 1)

for i in range(N - K):
    mi = bit.bisect_left(1)
    ma = bit.bisect_left(K)
    if P[i] != mi or P[K + i] < ma:
        count += 1
    bit.add(P[i], -1)
    bit.add(P[K + i], 1)

inc = 1
incseq = 0

for i in range(N - 1):
    if P[i] < P[i + 1]:
        inc += 1
        if inc == K:
            incseq += 1
    else:
        inc = 1

print(count - max(0, incseq - 1))

Buggy python submission (verdict: Time Limit Exceeded):
n,k = map(int,input().split())
P = [-1] + list(map(int,input().split())) + [10**6]
Q = [''.join(map(str,P))]
for i in range(1,n-k+1):
    q = P[:i] + sorted(P[i:i+k]) + P[i+k:]
    Q += [''.join(map(str,q))]
print(len(set(Q)))

Fixed submission:
class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, index):
        res = 0
        while index:
            res += self.tree[index]
            index -= index & -index
        return res

    def add(self, index, x):
        while index <= self.n:
            self.tree[index] += x
            index += index & -index

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1


N, K = map(int, input().split())
P = list(map(lambda x: int(x) + 1, input().split()))

bit = BinaryIndexedTree(N + 1)
count = 1

for i in range(K):
    bit.add(P[i], 1)

for i in range(N - K):
    mi = bit.bisect_left(1)
    ma = bit.bisect_left(K)
    if P[i] != mi or P[K + i] < ma:
        count += 1
    bit.add(P[i], -1)
    bit.add(P[K + i], 1)

inc = 1
incseq = 0

for i in range(N - 1):
    if P[i] < P[i + 1]:
        inc += 1
        if inc == K:
            incseq += 1
    else:
        inc = 1

print(count - max(0, incseq - 1))