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
n, k = map(int, input().split())
p = list(map(int, input().split()))
c = 0
l = [1] * (n - k + 1)
for i in range(k - 1):
    if p[i] > p[i + 1]:
        c += 1
if c == 0:
    l[0] = 0
for i in range(k - 1, n - 1):
    if p[i] > p[i + 1]:
        c += 1
    if p[i - k + 1] > p[i - k + 2]:
        c -= 1
    if c == 0:
        l[i - k + 2] = 0
k -= 1
qa = deque([])
a = [0] * (n - k + 1)
qb = deque([])
b = [0] * (n - k + 1)
for i in range(n):
    while qa and p[qa[-1]] > p[i]:
        qa.pop()
    while qb and p[qb[-1]] < p[i]:
        qb.pop()
    qa.append(i)
    qb.append(i)
    if qa[0] == i - k:
        qa.popleft()
    if qb[0] == i - k:
        qb.popleft()
    if i >= k - 1:
        a[i - k + 1] = p[qa[0]]
        b[i - k + 1] = p[qb[0]]
ans = l[0]
for i in range(n - k - 1):
    if (p[i] > a[i + 1] or b[i + 1] > p[i + k + 1]) and l[i + 1]:
        ans += 1
print(ans + 1 - min(l))