LeetCode 464 Can I Win - Problem Statement

Two players pick numbers from $1$ to $n$ (each number used at most once). The first player to reach a running total $\geq$ target wins. Can the first player guarantee a win? Example: $n = 10$, target $= 11$. Player 1 picks $10$. Player 2 picks any number. If Player 2 picks $1$, total is $11$ and Player 2 wins.

So Player 1 should pick differently... can they force a win? Here's where Bitmask DP meets Game Theory. The set of used numbers is a subset, perfect for bitmask. The game state is which numbers remain.