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)

from collections import deque
N,K=map(int,input().split())
P=list(map(int,input().split()))

out= deque()
l=len(P)
sp1=None

for n,p in enumerate(P):
    changed=None
    if n<=l-K:
        sp2=P[n:n+K]
        if sp1 is None or sp1 != sp2:
            s=sorted(sp2)
            if n==0:
                changed=s+P[n+K:]
            elif n==l-K:
                changed=P[0:n]+s
            else:
                changed=P[:n]+s+P[n+K:]
            if changed not in out:
                out.append(changed)
            sp1=sp2
        
print(len(out))