Problem: 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.

Examples

Input

5 3
0 2 1 4 3


Output

2


Input

4 4
0 1 2 3


Output

1


Input

10 4
2 0 1 3 7 5 4 6 8 9


Output

6

Solution (in PYTHON3):

Solution:
n,k=map(int,input().split())
P=[int(i) for i in input().split()]
import collections
from collections import deque
M1,M2=deque(),deque()
A1,A2=[],[]
M1.append(0)
for i in range(1,n):
  while M1:
    if P[M1[-1]]>P[i]:
      M1.pop()
    else:
      M1.append(i)
      break
  if not M1:
    M1.append(i)
  if M1[0]==i-k-1:
    M1.popleft()
  if i<k:
    continue
  else:
    A1.append(P[M1[0]])
M2.append(0)
for i in range(1,n):
  while M2:
    if P[M2[-1]]<P[i]:
      M2.pop()
    else:
      M2.append(i)
      break
  if not M2:
    M2.append(i)
  if M2[0]==i-k-1:
    M2.popleft()
  if i<k:
    continue
  else:
    A2.append(P[M2[0]])
ans=1
for i in range(n-k):
  if A1[i]==P[i] and A2[i]==P[i+k]:
    continue
  else:
    ans+=1
Q=[0]*n
for i in range(1,n):
  if P[i]>P[i-1]:
    Q[i]=Q[i-1]+1
  else:
    continue
count=0
for i in range(n):
  if Q[i]==k-1:
    count+=1
print(ans-max(0,count-1))