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.

5 3
0 2 1 4 3

2

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

4 4
0 1 2 3

1

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

6