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.

Examples

Input

5 3
0 2 1 4 3

Output

2

Input

4 4
0 1 2 3

Output

1

Input

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

Output

6

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