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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import deque
N, K = [int(x) for x in input().split()]
P = [int(x) for x in input().split()]
f = False
l = deque(P[:K-1])
cnt = 0
c = deque([])
for i in range(1, len(l)):
    c.append(1 if l[i-1]<l[i] else -1)
ccnt = 0
new = l[-1]
for p in P[K-1:]:
  l.append(p)
  bigger = p > new
  c.append(1 if bigger else -1)
  maxL = max(l)
  pre = l.popleft()
  if sum(c)==K-1:
    ccnt += 1
    c.popleft()
    new = p
    if pre < min(l):
      f = True
    else:
      f = False
    continue
  if f and p == maxL:
    cnt += 1
  if pre < min(l):
    f = True
  else:
    f = False
  c.popleft()
  new = p
if ccnt > 1:
  cnt += ccnt - 1
print(N - K + 1 - cnt)