Stone Division
Alice and Bob play a game with a pile of n stones and a set S = {s1, s2, ..., sk} of positive integers.
On each player's turn, they choose an integer x from S such that the current pile size is divisible by x. Then they divide the pile into x equal piles of size n/x stones. The player then chooses one of these piles to continue the game.
If no valid x exists, the player loses. Assuming both play optimally, return true if Alice (first player) wins.
Examples
Input: [6,[2,3]]
Output: true
Input: [12,[2,3,4]]
Output: false
Hints
This is an impartial combinatorial game. A position is losing if every possible move leads to a winning position for the opponent.
Use memoization: `dp[m]` stores whether a pile of size `m` is winning. For each divisor `x` in `S` where `m % x == 0`, check the resulting pile `m/x`.
The game reduces to standard impartial combinatorial game analysis on the recursive division tree.
Related Problems
Stone Division
Alice and Bob play a game with a pile of `n` stones and a set `S = {s1, s2, ..., sk}` of positive integers.