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:
n, k = map(int, input().split())
p = list(map(int, input().split()))

class SegmentTree:
    def __init__(self, n, func=lambda x, y: min(x, y), ide=float("inf")):
        self.n = 2 ** (n-1).bit_length()
        self.data = [ide] * (self.n*2)
        self.func, self.ide = func, ide
    
    def build(self, data):
        for i, x in enumerate(data):
            self.data[self.n+i] = x
        for i in range(self.n-1, 0, -1):
            self.data[i] = self.func(self.data[i*2], self.data[i*2+1])

    def update(self, i, x):
        i += self.n
        self.data[i] = x
        while i > 1:
            i //= 2
            self.data[i] = self.func(self.data[i*2], self.data[i*2+1])

    def query(self, l, r):
        l += self.n; r += self.n 
        res = self.ide
        while l < r:
            if l & 1:
                res = self.func(res, self.data[l])
                l += 1
            if r & 1:
                res = self.func(res, self.data[r-1])
            l //= 2; r //= 2
        return res
    
    def get(self, i):
        return self.data[self.n + i]

minst, maxst = SegmentTree(n), SegmentTree(n, lambda x, y: max(x, y), -float("inf"))
minst.build(p)
maxst.build(p)

ans = n - k + 1
for i in range(n-k):
    j = i + k
    if minst.query(i, j+1) == p[i] and maxst.query(i, j+1) == p[j]:
        ans -= 1

srted = [1] * n
cnt = 0
for i in range(n):
    if p[i] > p[i-1]: srted[i] = srted[i-1] + 1
    if srted[i] == k: cnt += 1

if cnt > 1: ans -= cnt - 1

print(ans)