A chain of n signal beacons is strung along a coastline, numbered 1 through n in the order they stand. Each beacon broadcasts at a fixed strength. A survey team wants to flag every "leading beacon": beacon i is a leading beacon if, among only two specific neighbors — the beacon exactly k positions earlier in the chain and the beacon exactly k positions later in the chain — its own strength is strictly greater than each of those two neighbors that actually exists inside the chain. If a beacon has neither of those neighbors within the chain (they would fall off either end), it counts as a leading beacon automatically. Compute the sum of the strengths of every leading beacon in the chain.

Input Format

• Line 1: two integers n and k
• Line 2: n integers strength_1 ... strength_n — the beacon strengths in chain order (1-indexed positions 1..n)

Output Format

A single integer: the sum of the strengths of all leading beacons.

Constraints

• 1 <= n <= 100
• 1 <= k <= n
• 1 <= strength_i <= 1000

5 2
1 2 3 4 5

9

1 1
7

7