RMO 2023 Problem 5

Let $n>k>1$ be positive integers. Determine all positive real numbers $a_1, a_2, \ldots, a_n$ which satisfy $$\sum_{i=1}^n \sqrt{\frac{k a_i^k}{(k-1) a_i^k+1}}=\sum_{i=1}^n a_i=n .$$