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 Python (3.4.3) (judge verdict: Wrong Answer)

N,K = map(int, input().split())
P = [int(p) for p in input().split()]

L = [0 for i in range(N-1)]
temp = P[0]
for i in range(1,N):
    if temp > P[i]:
        L[i-1] = 1
    temp = P[i]
        
L2 = []
for i in range(N-1-K+2):
    temp = []
    for j in range(i,K+i-1):
        temp += [L[j]]
    L2.append(temp)

zero = 0
cnt = 0
for i in range(len(L2)):
    j = 1
    c = 0
    if 1 not in L2[i]:
        zero += 1
    else:
        jud = 0
        for l in range(len(L2[i])):
            if L2[i][l] == 1:
                jud = 1
                break
        while j <= K-2 and i+j < len(L2) and jud == 0:
            temp = L2[i+j]
            temp.reverse()
            if L2[i] == temp:
                cnt += 1
            temp.reverse()
            j += 1
        
print(N-K+1-cnt-zero+1)