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
from collections import deque
from itertools import accumulate

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

def slide_min(A, K):
    res = []
    Q = deque()
    for i, a in enumerate(A):
        while Q and A[Q[-1]] > a:
            Q.pop()
        Q.append(i)
        if Q[0] == i - K:
            Q.popleft()
        res.append(Q[0])
    return res[K - 1:]

N, K = lr()
P = lr()
mi = slide_min(P, K)
ma = slide_min([-x for x in P], K)
new_pattern = [not (mi == i and ma == i+K) for i, (mi, ma) in enumerate(zip(mi, ma[1:]))]
# Trueの時は新しいパターンが登場
increase = [0] + list(accumulate(x<y for x, y in zip(P, P[1:])))
# K区間で常に上昇
stable_increase = [y-x == K-1  for x, y in zip(increase, increase[K-1:])]
answer = 1 + sum([x for x, y in zip(new_pattern, stable_increase[1:]) if not y])
if not stable_increase[0] and any(stable_increase):
    answer += 1
print(answer)