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)

s = input().split(" ")
n = int(s[0])
k = int(s[1])
sp = input().split(" ")
p = [int(pstr) for pstr in sp]
num = 0
ident = False
M = max(p[:k])
m = min(p[:k])


for i in range(n - k + 1):
    for j in range(k - 1):
        if p[i + j] > p[i + j +1]:
            break
    else:
        if not ident:
            ident = True
            num += 1
        continue

    if i == 0:
        num += 1
        continue
    else:
        if p[i - 1] > min(p[i:i + k - 1]) or p[i + k - 1] < max(p[i:i + k - 1]):
            num += 1      
    

print(num)