Poker Nim

Poker Nim is a variant of Nim. In addition to removing stones from a pile, a player may also add stones to a pile, up to k stones per move. A player may either remove any positive number of stones from a single pile, or add 1 to k stones to a single pile. The player who takes the last stone wins. Determine if the first player has a winning strategy.

Examples
Input: [[1,2,3],3]
Output: false
Hints

Poker Nim

Poker Nim is a variant of Nim. In addition to removing stones from a pile, a player may also **add** stones to a pile, up to `k` stones per move. A player may either remove any positive number of stones from a single pile, or add 1 to `k` stones to a single pile. The player who takes the last stone wins. Determine if the first player has a winning strategy.