Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

5 3
0 2 1 4 3

Sample Output 1

2

Two permutations can be produced as P after the operation: (0,1,2,4,3) and (0,2,1,3,4).

Sample Input 2

4 4
0 1 2 3

Sample Output 2

1

Sample Input 3

10 4
2 0 1 3 7 5 4 6 8 9

Sample Output 3

6

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

class SWAG():
    __slots__='unit','f','fold_r','fold_l','data_r','data_l'
    def __init__(self,unit,f,data):
        self.unit=unit
        self.f=f
        self.construct(data)
    def construct(self,data):
        self.fold_r=[self.unit]
        self.fold_l=[self.unit]
        self.data_r=[]
        self.data_l=[]
        sep=len(data)//2
        for t in data[sep+1:]:
            self.append(t)
        for t in data[sep::-1]:
            self.appendleft(t)
    def append(self,x):
        self.fold_r.append(self.f(self.fold_r[-1],x))
        self.data_r.append(x)
    def appendleft(self,x):
        self.fold_l.append(self.f(self.fold_l[-1],x))
        self.data_l.append(x)
    def pop(self):
        if not self.data_r:
            self.construct(self.data_l[::-1])
        self.fold_r.pop()
        return self.data_r.pop()
    def popleft(self):
        if not self.data_l:
            self.construct(self.data_r)
        self.fold_l.pop()
        return self.data_l.pop()
    def fold_all(self):
        return self.f(self.fold_r[-1],self.fold_l[-1])
n,k,*p=map(int,open(0).read().split())
c=[0]
for a,b in zip(p,p[1:]):c+=c[-1]+(a<b),
*c,f=[b-a==k-1for a,b in zip(c,c[k-1:])]
x=not f
s_min=SWAG(10**18,min,p[:k-1])
s_max=SWAG(0,max,p[1:k])
for i,(a,b,c)in enumerate(zip(p,p[k:],c)):
    f|=c
    s_min.append(p[i+k-1])
    s_max.append(b)
    if not c and(a!=s_min.fold_all()or b!=s_max.fold_all()):x+=1
    s_min.popleft()
    s_max.popleft()
print(x+f)