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)

N, K = map(int,input().split())
p_list = list(map(int, input().split()))
initial_number = N-K+1
ini_sw = 0
fin_sw = 0
count_1 = 0
count_2 = 0
for i in range(initial_number):
    p_range = p_list[i:i+K]
    p_range_asc = sorted(p_range)
    if p_range[-1] == p_range_asc[-1]:
        fin_sw = 1
    else:
        fin_sw = 0
    if fin_sw == 1 and ini_sw == 1:
        count_1 += 1
    if p_range[0] == p_range_asc[0]:
        ini_sw = 1
    else:
        ini_sw = 0
    
    if p_range == p_range_asc:
        count_2 += 1
if count_2 >= 1:
    count_2 -=1
output = initial_number - (count_1 + count_2) 
print(output)