Apply Operations on Array to Maximize Sum of Squares

You're allowed to repeatedly pair elements and replace them with their bitwise AND and OR, which effectively transfers set bits between numbers; maximize the sum of squares of any k elements after any sequence of such operations. The core challenge is to optimally redistribute bit counts across the array (using per-bit frequencies) to build k large numbers that maximize the sum of squares under constraints n ≤ 1e5 and nums[i] ≤ 1e9.