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: Runtime Error)

N,K = map(int,input())
P = list(map(int,input().split()))
Q = P[:K]
R = sorted(Q)
if R == Q:
    f == 1
if N == K:
    ans = 1
else:
    ans = 1
    m = R[0]
    for i in range(K,N):
        x = Q.pop(0)
        y = P[i]
        Q.append(y)
        R = Q.sorted()
        if R[-1] == y:
            if m == x:
                continue
            else:
                if f == 0:
                    ans += 1
        else:
            ans += 1
        if R == Q:
            f = 1
print(ans)