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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