AMO-Bench 2025 Problem 6

Let ${x}_{1},{x}_{2},\cdots ,{x}_{2024}$ be positive real numbers such that ${x}_{k} + {x}_{m} \geq {km}$ for any $1 \leq k < m \leq {2024}$. Find the minimum value of ${x}_{1} + {x}_{2} + \cdots + {x}_{2024}$.