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 deque

class SlideMin:
    def __init__(self, leng):
        self.que = deque([])
        self.leng = leng

    def top(self):
        return self.que[0]

    def getQue(self):
        return self.que

    def update(self, index, value=0):
        while self.que:
            if self.que[-1][1] >= value:
                self.que.pop()
            else:
                break

        self.que.append((index, value))

        if self.que[0][0] == index - self.leng:
            self.que.popleft()

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

maxQ = SlideMin(K)
minQ = SlideMin(K)

for i in range(K):
    maxQ.update(i, -P[i])
    minQ.update(i, P[i])

ans = 1
hasSame = False
seq = 1
for i in range(1, K):
    if P[i - 1] < P[i]:
        seq += 1
    else:
        seq = 1
if seq >= K:
    hasSame = True

for left in range(N - K):
    right = left + K

    if P[right - 1] < P[right]:
        seq += 1
    else:
        seq = 1

    maxQ.update(right, -P[right])

    if left == minQ.top()[0] and right == maxQ.top()[0]:
        pass
    else:
        if seq < K:
            ans += 1
        else:
            if not hasSame:
                hasSame = True
                ans += 1

    minQ.update(right, P[right])

print(ans)