Stone Division II

Alice and Bob play a game with n piles of stones. On each turn, a player picks a pile of size m, then chooses a divisor d of m where 1 < d <= m (strictly greater than 1). They split the pile into d equal-sized piles of size m/d. If a pile has size 1, it cannot be split and is removed from play. A player who cannot make a move loses. Both play optimally — determine if Alice (first player) has a winning strategy.

Examples
Input: [1,[1]]
Output: false
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Stone Division II

Alice and Bob play a game with n piles of stones. On each turn, a player picks a pile of size m, then chooses a divisor d of m where 1 < d <= m (strictly greater than 1). They split the pile into d equal-sized piles of size m/d. If a pile has size 1, it cannot be split and is removed from play. A player who cannot make a move loses. Both play optimally — determine if Alice (first player) has a winning strategy.