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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分