Leetcode 2731. Movement of Robots

Robots move 1 unit/sec left or right and instantly swap directions on collision; compute the sum of pairwise distances after d seconds modulo 1e9+7. Using the observation that collisions only swap identities (so final positions are nums[i] ± d), the task reduces to efficiently computing the sum of absolute differences among those final coordinates (e.g., via sorting and prefix sums).