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: Accepted)

from collections import deque


N, K = map(int, input().split())
P = list(map(int, input().split()))

smin = deque()
smax = deque()
x = 0
r = 0
r2 = 0

for i, p in enumerate(P):
    while len(smin) > 0 and P[smin[-1]] > p:
        smin.pop()
    smin.append(i)
    if smin[0] <= i - K:
        smin.popleft()
    while len(smax) > 0 and P[smax[-1]] < p:
        smax.pop()
    smax.append(i)
    if smax[0] <= i - K:
        smax.popleft()
    if i > 0 and P[i-1] < P[i]:
        x = min(x + 1, K - 1)
    else:
        x = 0
    if i == K-1 or (i >= K and not (P[i - K] < P[smin[0]] and smax[0] == i)):
        if x != K-1:
            r += 1
        else:
            r2 = 1
print(r + 1 if r2 else r)