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 = list(map(int, input().split()))
xs = list(map(int, input().split()))
from collections import deque
def slide_max(k, l):
    rs, rrs = [], set()
    dq = deque()
    for i, x in enumerate(l):
        while True:
            if not len(dq):
                dq.append(i)
                break
            lxi = dq[-1]
            if x < l[lxi]:
                dq.append(i)
                break
            dq.pop()
        if i+1 < k:
            continue
        sxi = dq[0]
        rs.append(l[sxi])
        if sxi == (i + 1 - k):
            dq.popleft()
    return rs

def slide_min(k, l):
    rs = []
    rrs = set()
    dq = deque()
    for i, x in enumerate(l):
        while True:
            if not len(dq):
                dq.append(i)
                break
            lxi = dq[-1]
            if x > l[lxi]:
                dq.append(i)
                break
            dq.pop()
        if i+1 < k:
            continue
        if len(dq) == k:
            rrs.add(i+1-k)
        sxi = dq[0]
        rs.append(l[sxi])
        if sxi == (i + 1 - k):
            dq.popleft()
    return rs, rrs

maxs, (mins, ns) = slide_max(k, xs), slide_min(k, xs)
r = 1
for i, (s, x) in enumerate(zip(xs, xs[k:])):
    if (x != maxs[i+1] or s != mins[i]) and (i+1 not in ns): 
        r+=1
if (0 not in ns) and (len(ns) > 0):
    r += 1
print(r)