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: Wrong Answer)

from bisect import bisect_left as bl
N, K = map(int, input().split())
p = list(map(int, input().split()))
unsorted = []
res = 0
for i in range(N - 1):
  if p[i - 1] > p[i]:
    unsorted.append(i)
unsorted.sort()
visited = set()
#print(unsorted)
for i in range(N - K + 1):
  l = bl(unsorted, i)
  r = min(bl(unsorted, i + K - 1), N - 1)
  #print(l, r)
  if (l, r) in visited:
    continue
  else:
    res += 1
    visited.add((l, r))
print(res)