Count Players Reaching End with Moving Watchers

You are given a 1D line of L cells indexed 0 to L-1. The target end cell is L-1.

There are W watchers and P players, each with initial integer positions.

A time horizon T is given, representing the number of unit-time steps.

An unsorted list flipTimes contains integer timestamps. At each timestamp t in flipTimes, all watchers reverse their direction.

Movement Model (Discrete Time):

• Time steps are t = 0, 1, ..., T-1.
• Each watcher has a facing direction (LEFT or RIGHT). All watchers start facing LEFT at time 0.
• At the start of each step t, if t is in flipTimes, all watchers reverse direction.
• Watching Rule: At step t, a watcher at position x:
  • If facing LEFT, watches all cells < x.
  • If facing RIGHT, watches all cells > x. A player is considered watched if at least one watcher watches the player's current cell.
• Player Move: During step t, each player attempts to move one cell to the right (from p to min(p+1, L-1)). However, if the player is watched at the start of the step, the player cannot move and stays in place.
• Watcher Move: After all players have attempted to move, each watcher moves one cell in its facing direction:
  • LEFT: x = max(x-1, 0)
  • RIGHT: x = min(x+1, L-1)

Task:

After performing exactly T steps, return the count of players that are at cell L-1.

Notes/Clarifications:

• Multiple players and watchers may occupy the same cell.
• flipTimes may contain duplicates and is not sorted.

Constraints:

• 1 <= L <= 2e5
• 0 <= W, P <= 2e5
• 0 <= T <= 2e5
• 0 <= flipTimes[i] <= T-1