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:
from collections import deque
n,k = map(int,input().split())
a = list(map(int,input().split()))
k -= 1
mnlist = []
q = deque([0])
for i in range(1,k):
  while q:
    x = q.pop()
    if a[i]>a[x]:
      q.append(x)
      q.append(i)
      break
  if not q:
    q.append(i)

for i in range(k,n+1):
  t = q.popleft()
  mnlist.append(a[t])
  if t != i-k:
    q.appendleft(t)
  if i == n:
    break
  while q:
    x = q.pop()
    if a[i]>a[x]:
      q.append(x)
      q.append(i)
      break
  if not q:
    q.append(i)
mxlist = []
q = deque([0])
for i in range(1,k):
  while q:
    x = q.pop()
    if a[i]<a[x]:
      q.append(x)
      q.append(i)
      break
  if not q:
    q.append(i)

for i in range(k,n+1):
  t = q.popleft()
  mxlist.append(a[t])
  if t != i-k:
    q.appendleft(t)
  if i == n:
    break
  while q:
    x = q.pop()
    if a[i]<a[x]:
      q.append(x)
      q.append(i)
      break
  if not q:
    q.append(i)
ans = n-k
r = set()
for i in range(1,n-k):
  if a[i-1]<mnlist[i] and mxlist[i]<a[i+k]:
    r.add(i)
flg = 0
flg2 = 0
for i in range(1,n):
  if a[i-1] < a[i]:
    flg += 1
  else:
    flg = 0
  if flg >= k:
    r.add(i-k)
    flg2 = 1
print(ans-len(r)+flg2)