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)

import numpy as np
import copy
N, K = map(int,input().split(' '))
P = np.array(list(map(int,input().split(' '))))
ans = []
for i in range(N-K+1):
  p = P
  q = copy.deepcopy(p)
  temp = np.sort(p[i:i+K])
  q[i:i+K] = temp
  if i == 0:
    t = copy.deepcopy(q)
    ans.append(t)
  else:
    for j in range(len(ans)):
      if not all(q == ans[j]):
        t = copy.deepcopy(q)
        ans.append(t)
        break
print(len(ans))