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()))
from collections import deque
smin,smax=deque(),deque()
x,r,r2=0,0,0
for i,p in enumerate(P):
    while len(smin)>0 and P[smin[-1]]>p:
        smin.pop()
    smin.append(i)
    if smin[0]<=i-K:
        smin.popleft()
    while len(smax)>0 and P[smax[-1]]<p:
        smax.pop()
    smax.append(i)
    if smax[0]<=i-K:
        smax.popleft()
    if i>0 and P[i-1]<P[i]:
        x=min(x+1,K-1)
    else:
        x=0
    if i==K-1 or (i>=K and not (P[i-K]<P[smin[0]] and smax[0]==i)):
        if x!=K-1:
            r+=1
        else:
            r2=1
print(r+1 if r2 else r)