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 (i.e., buying at most k times and selling at most k times).

Note: Multiple transactions cannot be held simultaneously — the current stock must be sold before purchasing 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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