# A game of 2's

Sharky and Ivan are playing a strange game, with Sharky going first.

They start with a heap of 420 coins. They then take turns to remove some of the coins using the two rules below.

Given that the number of coins in the pile is $$k,$$ you may either

1. remove the largest power of 2 less than $$k,$$ if $$k$$ is not a power of 2, or
2. remove half the coins only if $$k$$ is even.

If a person cannot make a legal move, they lose. Who has the winning strategy?

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