Sorting a Segment

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N K P_0 P_1 \cdots P_{N-1}

outputFormat

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

样例

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

6