Problem:
Score : 700 points

Problem Statement

Snuke has a permutation (P_0,P_1,\cdots,P_{N-1}) of (0,1,\cdots,N-1).

Now, he will perform the following operation exactly once:

Choose K consecutive elements in P and sort them in ascending order.

Find the number of permutations that can be produced as P after the operation.

Constraints

2 \leq N \leq 200000

2 \leq K \leq N

0 \leq P_i \leq N-1

P_0,P_1,\cdots,P_{N-1} are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
P_0 P_1 \cdots P_{N-1}

Output

Print the number of permutations that can be produced as P after the operation.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

from heapq import heappush, heappop

N, K = map(int, input().split())
A = list(map(int, input().split()))

h_max = []
h_min = []
for i in range(K):
  heappush(h_min,  A[i])
  heappush(h_max, -A[i])

check = [0] * (N + 1)
tmp = [0] * N
tmp[0] = 1
for i in range(N - K):
  
  a_min =  heappop(h_min)
  a_max = -heappop(h_max)
  while check[a_min]:
    a_min =  heappop(h_min)
  while check[a_max]:
    a_max = -heappop(h_max)
  if A[i] == a_min and A[i + K] > a_max:
    tmp[i + 1] -= 1
  check[A[i]] = 1
  heappush(h_min,  a_min)
  heappush(h_max, -a_max)  
  heappush(h_min,  A[i + K])
  heappush(h_max, -A[i + K])  
  tmp[i + 1] += 1

B = [0]
for i in range(1, N):
  if A[i] > A[i - 1]:
    B.append(1)
  else:
    B.append(0)

sum_B = sum(B[1: K])
flag = 0
for i in range(N - K + 1):
  if sum_B == K - 1:
    if tmp[i]:
      flag = 1
      tmp[i] = 0
  if i == N - K:
    break
  sum_B = sum_B - B[i + 1] + B[i + K]

print(sum(tmp) + flag)