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 heapq import heappush, heappop
N, K , *P = map(int, open(0).read().split())
mhq = []
Mhq = []
for c in P[:K]:
  heappush(mhq,c)
  heappush(Mhq,-c)

ans = 1
log = set()
for i,c in enumerate(P[K:]):
  while mhq[0] in log:
    heappop(mhq)
  while -Mhq[0] in log:
    heappop(Mhq)
  d = P[i]
  m = mhq[0]
  M = -Mhq[0]
  log.add(d)
  heappush(mhq,c)
  heappush(Mhq,-c)
  if not (m==d and M<c):
    ans += 1
p = P[0]
m = 1
x = 0
for c in P[1:]:
  if p<c:
    m += 1
  else:
    if m>=K:
      x += 1
    m = 1
  p = c
if m>=K:
  x += 1
if x!=0:
  ans -= x-1
print(ans)