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