Crosswalk Controller

Work out what a pedestrian crossing's signal shows at given moments, given when the walk button was pressed.

The crossing lights a single phase at every whole minute t >= 0. The phases, in cycle order, are GREEN (cars may go), YELLOW, WALK (pedestrians may cross) and FLASH (pedestrians must finish crossing), and then back to GREEN. timings = [g, y, w, f] gives the lengths in minutes: YELLOW lasts exactly y minutes, WALK exactly w, FLASH exactly f. GREEN always lasts at least g minutes, and at time 0 it has just begun.

A phase that begins at minute s and lasts d minutes is shown at minutes s .. s + d - 1; the next phase starts at s + d.

The button works like this. A press at minute p is looked at after any phase change that happens at minute p:

• During GREEN it registers a request, unless a request is already waiting (then it does nothing).
• During YELLOW or WALK it does nothing: the walk is already on its way or under way.
• During FLASH it registers a request for the next green period; the pedestrian has just missed the walk.

When GREEN has a request waiting, it ends as soon as both conditions hold: it has lasted at least g minutes, and the request exists. If the request was registered at minute p and the current GREEN began at minute b, the next YELLOW therefore starts at minute max(p, b + g). A request that was registered during FLASH is already waiting when the next GREEN begins, so that GREEN lasts exactly g minutes. With no request, GREEN lasts forever.

Input: timings, as above; presses, the minutes at which the button was pressed, in non-decreasing order (duplicates are possible); queries, minutes to report, in any order.

Output: a list with the phase name ("GREEN", "YELLOW", "WALK" or "FLASH") shown at each query minute, in query order.