Given an integer array prices, where prices[i] represents the price of a stock on the i^{th} day, and an integer k, determine the maximum profit achievable by completing at most k transactions.

A transaction consists of buying the stock on one day and selling it on a later day.

Note: You cannot hold multiple stocks simultaneously. You must sell the current stock before buying again.

Constraints:

• $1 \leq$ k $\leq 10^2$

• $1 \leq$ prices.length $\leq 10^3$

• $0 \leq$ prices[i] $\leq 10^3$

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