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: Time Limit Exceeded)

n,k = map(int, input().split())
p_list = list(map(int, input().split()))

p_before = 200001
up = 0

mins = [0]*(n+1-k)
maxs = [0]*(n+1-k)

for i in range(n+1-k):
    temp = p_list[i:i+k]
    mins[i] = min(temp)
    maxs[i] = max(temp)

mins = mins[:-1]
maxs = maxs[1:]

origin = 0
not_origin = 0

for p in p_list[:k]:
    if p_before < p:
        up += 1
    else:
        up=0
    p_before = p*1

    if p == p_list[k-1]:
        if up >= k-1:
            origin = 1
        else:
            not_origin = 1


for p,i in zip(p_list[k:], range(k,n)):
    if p_before < p:
        up += 1
    else:
        up=0
    p_before = p*1

    if up >= k-1:
        origin = 1
    else:
        if p_list[i-k] == mins[i-k]:
            if p_list[i] != maxs[i-k]:
                not_origin += 1
        else:
            not_origin += 1


print(origin + not_origin)