Reservoir Tide Cycle

Track a tidal holding pond whose gate is operated on the same schedule every day, for a very long time.

The pond holds at most cap units of water and starts with start units. Every day the gate applies the same list events in order. A positive event e lets e units flow in; a negative event releases -e units.

• If an inflow would take the level above cap, the pond ends at cap and the excess is lost (counted as overflow).
• If a release would take the level below 0, the pond ends at 0 and the part that could not be released is the shortfall (counted).
• Clamping happens after each single event, not once per day.

Report the situation after days full days.

Input: cap, start, events, days.

Output: [level, lost, shortfall]: the water level after the last day, and the total overflow and total shortfall over all days days.

days can be as large as 10^12, so the days cannot be played out one at a time.