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)

import sys
import heapq
if sys.platform =='ios':
    sys.stdin=open('input_file.txt')

N,k=map(int,input().split())

p=list(map(int,input().split()))
q=[n*(-1) for n in p]
cnt=1

for i in range(N-k-1):
	heapq.heapify(p[i:i+k])
	heapq.heapify(q[i+1:i+k+1])
	if heapq.heappop(p[i:i+k])==p[i] and heapq.heappop(q[i+1:i+k+1])==q[i+k+1]:
		cnt+=0
	else:
		cnt+=1
	
print(cnt)