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:
import sys
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 7)

from collections import deque

N,K,*P=map(int,sys.stdin.read().split())

Kmin = []
deq = deque()
for i in range(K):
    while deq and P[deq[-1]] > P[i]:
        deq.pop()
    deq.append(i)
Kmin.append(deq[0])
for i in range(K,N):
    if deq[0] == i-K:
        deq.popleft()
    while deq and P[deq[-1]] > P[i]:
        deq.pop()
    deq.append(i)
    Kmin.append(deq[0])

Kmax = []
deq = deque()
for i in range(K):
    while deq and P[deq[-1]] < P[i]:
        deq.pop()
    deq.append(i)
Kmax.append(deq[0])
for i in range(K,N):
    if deq[0] == i-K:
        deq.popleft()
    while deq and P[deq[-1]] < P[i]:
        deq.pop()
    deq.append(i)
    Kmax.append(deq[0])

is_new_seq = [Kmin[i] != i or Kmax[i+1] != i+K for i in range(N-K)]

is_new_seq

import itertools
incr = [1 if x<y else 0 for x,y in zip(P,P[1:])]
incr_cum = [0] + list(itertools.accumulate(incr))
is_stable = [y-x==K-1 for x,y in zip(incr_cum,incr_cum[K-1:])]

is_new_seq = [x&(not y) for x,y in zip(is_new_seq,is_stable[1:])]

answer = sum(is_new_seq)
if not is_stable[0]:
    answer += 1
    if any(is_stable):
        answer += 1
else:
    answer += 1
print(answer)