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:
class BinaryIndexedTree():  #1-indexed
    def __init__(self, n):
        self.n = n
        self.tree = [0 for _ in range(n + 1)]

    def sum(self, index):
        res = 0
        while index:
            res += self.tree[index]
            index -= index & -index
        return res

    def add(self, index, x):
        while index <= self.n:
            self.tree[index] += x
            index += index & -index

    def bisect_left(self, x):
        if x <= 0: return 0
        res, tmp = 0, 2**((self.n).bit_length() - 1)
        while tmp:
            if res + tmp <= self.n and self.tree[res + tmp] < x:
                x -= self.tree[res + tmp]
                res += tmp
            tmp >>= 1
        return res + 1


N, K = map(int, input().split())
P = list(map(lambda x: int(x) + 1, input().split()))

bit = BinaryIndexedTree(N + 1)
count = 1

for i in range(K):
    bit.add(P[i], 1)

for i in range(N - K):
    mi = bit.bisect_left(1)
    ma = bit.bisect_left(K)
    if P[i] != mi or P[K + i] < ma:
        count += 1
    bit.add(P[i], -1)
    bit.add(P[K + i], 1)

inc = 1
incseq = 0

for i in range(N - 1):
    if P[i] < P[i + 1]:
        inc += 1
        if inc == K:
            incseq += 1
    else:
        inc = 1

print(count - max(0, incseq - 1))