Fix the server movement step for a shooter

Your multiplayer shooter's server accepted each client's claimed position, so speed hacks and teleports were the protocol working as written. The fix makes the server authoritative: clients send only an input, and the server moves the player itself under a speed cap and inside the world's bounds.

An assistant wrote simulate_player_movement(intents, max_speed, dt, min_x, max_x). It is in the editor. It has a bug. Find it and fix it.

Input and output:

• intents: one input per tick, in order, nominally from -1 (full left) to 1 (full right). A hacked client can send anything.
• max_speed: the most distance per second, dt: the tick length in seconds.
• min_x, max_x: the world's bounds on this axis.
• Return the player's position after each tick, one per intent.

Rules the tests check:

• If min_x is greater than max_x, swap them.
• A tick moves the player by intent * max_speed * dt. If max_speed * dt is negative, use 0.
• Clamp each intent to the range -1 to 1 first.
• The player spawns at 0, clamped into the bounds.
• After every tick, clamp the position into the bounds. The next tick starts from that clamped position.
• Answers within 0.000001 of the expected value pass.