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()))

if n == k:
    print(1)
    exit()

def slide_min(n, k, p):
    res = [0] * n
    deq = [0] * n
    s = 0
    t = 0
    for i in range(n):
        while s < t:
            if p[deq[t-1]] >= p[i]:
                t -= 1
            else:
                break
        deq[t] = i
        t += 1
        if i-k+1 >= 0:
            res[i-k+1] = p[deq[s]]
            if deq[s] == i-k+1:
                s += 1
    return res

def slide_max(n, k, p):
    res = [0] * n
    deq = [0] * n
    s = 0
    t = 0
    for i in range(n):
        while s < t:
            if p[deq[t-1]] < p[i]:
                t -= 1
            else:
                break
        deq[t] = i
        t += 1
        if i-k+1 >= 0:
            res[i-k+1] = p[deq[s]]
            if deq[s] == i-k+1:
                s += 1
    return res

s_min = slide_min(n, k, p)
s_max = slide_max(n, k, p)

ans = 1
for i in range(n-k):
    if p[i] > s_min[i] or p[i+k] != s_max[i+1]:
        ans += 1

mode = 0
count = 0
e = 0
for i in range(n-1):
    if p[i] < p[i+1]:
        if mode == 0:
            count = 2
            mode = 1
        else:
            count += 1
    else:
        mode = 0
        if count >= k:
            e += 1
            count = 0

if mode == 1 and count >= k:
    e += 1

if e > 1:
    ans -= e-1

print(ans)