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 = map(int, input().split())
P = [int(i) for i in input().split()]

dp = [0] * N
dp[0] = 1
for i in range(1, N) :
    if P[i] > P[i-1] :
        dp[i] = dp[i-1] + 1
    else :
        dp[i] = 1
        
ma = []
mi = []

for i in range(K) :
    heappush(ma, (-P[i], i))
    heappush(mi, (P[i], i))

if dp[K-1] == K :
    ret = 0
else :
    ret = 1
    
for i in range(K, N) :
    heappush(ma, (-P[i], i))
    heappush(mi, (P[i], i))
    
    while ma[0][1] < i - K :
        heappop(ma)
    while mi[0][1] < i - K :
        heappop(mi)
        
    if dp[i] < K and (P[i-K] != mi[0][0] or P[i] != -ma[0][0]) :
        ret += 1

if sum([dp[i] >= K for i in range(N)]) > 0 :
    ret += 1

print(ret)