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 heapq

N,K = map(int,input().split())

P = list(map(int,input().split()))

minlis = []
maxlis = []
endflag = [False] * N

ans = 1

for i in range(K):

    heapq.heappush(minlis,P[i])
    heapq.heappush(maxlis,-1 * P[i])

for i in range(N - K):

    flag = False

    endflag[P[i]] = True
    if minlis[0] != P[i]:
        flag = True

    while endflag[minlis[0]]:
        heapq.heappop(minlis)

    if P[i+K] <= -1 * maxlis[0]:
        flag = True

    while endflag[-1 * maxlis[0]]:
        heapq.heappop(maxlis)

    

    heapq.heappush(minlis,P[i+K])
    heapq.heappush(maxlis,-1 * P[i+K])



    if flag:
        ans += 1

kaburi = 0
P.append(-2)
now = 0
nmax = -1
for i in range(N+1):
    if nmax < P[i]:
        now += 1
        nmax = P[i]
    else:
        if now >= K:
            kaburi += 1 #max(0 , now - K + 1)
        now = 1
        nmax = P[i]
        
#print (ans,kaburi)
if kaburi >= 2:
    print (ans - kaburi + 1)
else:
    print (ans)