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 = []
    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 = []
    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

maxs, mins = slide_max(k, xs), slide_min(k, xs)
aa, bb = xs[:k], xs[k:]

b, nb, bx = aa[0], aa[1], aa[-1]
ba = None
c = 1
for a in aa:
    if ba == None:
        ba = a
        continue
    if a > ba:
        c += 1
    else:
        c = 1
    ba = a

rok = False
if c == k:
    rok = True

r = 1
bs = xs[0]
for i, (s, x) in enumerate(zip(xs[1:], bb)):

    if x > bx:
        c = min(c+1, k)
    else:
        c = 1
    bx = x

    if c == k:
        if not rok:
            r += 1
        rok = True
        continue

    if x != maxs[i+1]: 
        r+=1
    elif bs != mins[i]:
        r+=1
    bs = s

print(r)