You are given an integer array prices where prices[i] is the price of a given stock on day i, and an integer k.

You may complete at most k transactions. Each transaction can be one of the following two types:

1. Normal transaction: Buy the stock on day i and sell it on day j with i < j, achieving a profit of prices[j] $-$ prices[i].

2. Short selling transaction: Sell the stock on day i and buy it back on day j with i < j, achieving a profit of prices[i] $-$ prices[j].

You cannot engage in multiple transactions simultaneously. That is, you must finish your current transaction before initiating a new one.

Return the maximum profit you can achieve.

Constraints:

• $2 \leq$ prices.length $\leq 10^3$

• $1 \leq$ prices[i] $\leq 10^9$

• $1 \leq$ k $\leq$ prices.length $/ 2$

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