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 Counter
from heapq import heappush, heappop
N,K,*P = map(int, open(0).read().split())
i = 0
ans = 1
Cnt = Counter(P[:K])
mls = []
Mls = []
for i in range(K):
  heappush(mls,P[i])
  heappush(Mls,-P[i])
for i in range(N-K):
  Cnt[P[i]] -= 1
  Cnt[P[i+K]] += 1
  if not (P[i]==mls[0] and P[i+K]>=-Mls[0]):
    ans += 1
  heappush(mls,P[i+K])
  heappush(Mls,-P[i+K])
  while Cnt[mls[0]]==0:
    heappop(mls)
  while Cnt[-Mls[0]]==0:
    heappop(Mls)
i = 0
flag = False
for j in range(1,N):
  if P[j]<P[j-1]:
    if j-i>=K:
      ans -= 1
      flag = True
    i = j
if j-i>=K-1:
  flag = True
  ans -= 1
if flag:
  ans += 1
print(ans)