Frog 2

Source: AtCoder

Version: Phuoc Hung OJ Extended

Problem Statement

There are $N$ stones with heights $h_i$. From stone $i$, the frog may jump to any of $i+1,\ldots,i+K$. A jump from $i$ to $j$ costs $|h_i-h_j|$. Find the minimum cost from stone 1 to stone $N$.

Input

Line 1 contains $N$ and $K$. Line 2 contains $N$ integers $h_1,\ldots,h_N$.

Output

Print the minimum total cost.

Subtasks

• Subtask 1 — 20 points: 2 <= N <= 20; 1 <= K <= 5.
• Subtask 2 — 30 points: 2 <= N <= 2000; 1 <= K <= 30.
• Subtask 3 — 50 points: 2 <= N <= 100000; 1 <= K <= 100; 1 <= h_i <= 10000.

Examples

Input

5 3
10 30 40 50 20

Output

30

Explanation

The route $1\to2\to5$ costs $20+10=30$, and no cheaper route exists.