Frog 2

There are N stones, numbered 1, 2, \ldots, N. For each i (1 \leq i \leq N), the height of Stone i is h_i.

There is a frog who is initially on Stone 1. He will repeat the following action some number of times to reach Stone N:

• If the frog is currently on Stone i, jump to one of the following: Stone i + 1, i + 2, \ldots, i + K. Here, a cost of |h_i - h_j| is incurred, where j is the stone to land on.

Find the minimum possible total cost incurred before the frog reaches Stone N.

Constraints

• All values in input are integers.
• 2 \leq N \leq 10^5
• 1 \leq K \leq 100
• 1 \leq h_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N K h_1 h_2 \ldots h_N

Output

Print the minimum possible total cost incurred.

Examples

Input

5 3 10 30 40 50 20

Output

30

Input

3 1 10 20 10

Output

20

Input

2 100 10 10

Output

0

Input

10 4 40 10 20 70 80 10 20 70 80 60

Output

40

inputFormat

input are integers.

• 2 \leq N \leq 10^5
• 1 \leq K \leq 100
• 1 \leq h_i \leq 10^4

Input

Input is given from Standard Input in the following format:

N K h_1 h_2 \ldots h_N

outputFormat

Output

Print the minimum possible total cost incurred.

Examples

Input

5 3 10 30 40 50 20

Output

30

Input

3 1 10 20 10

Output

20

Input

2 100 10 10

Output

0

Input

10 4 40 10 20 70 80 10 20 70 80 60

Output

40

样例

2 100
10 10

0