According to the discussion boards, the expected solution for this problem is O(NM + K(N+M)). There was some talk about poor test cases being fixed, but I think the problem itself may be flawed.
When a pulse occurs at a time point that could potentially block Spiff, that pulse may become synchronized with Spiff (since they move at the same speed) along both the X & Y axis’, effectively segregating some lower-right portion of the grid and making the goal unreachable for all paths.
Also blasters appear to be independent (i.e., there are no cases where the combined effects of blasters would block Spiff where individually they could not), making a synchronized pulse the only way to stop Spaceman Spiff.
Therefore, the problem becomes: Will Spiff synchronize with any reachable pulse? Which can be solved in O(K) (See solution here). Is this right?