Statement 1.

A player ALWAYS perform:

 - "even" operations (e.g. ..., 2^62->2^61, 2^60->2^59, ..., 2^4->2^3, 2^2->2^1, STOP). He's named "even" player below.

 - "odd" operations (e.g. ..., 2^61->2^60, ..., 2^3->2^2, 2^1->2^0, STOP). He's named "odd" player below.

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Statement 2.

In addition to statement 1, first player (i.e. Louise) can initially hold a number (called "start" number) different from a "2-power" numbers. In this case, first player performs an ADDITIONAL pre-operation to reduce "start" number to the largest "2-power" number.

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Statement 3.

"Odd" player ALWAYS wins because he perform the last valid turn (i.e. from 2^1 to 2^0). In interest of clarity:

 - "even" player is therefore re-named "loser-even" player.

 - "odd" player is therefore re-named "winner-odd" player.

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This said, for ALL "start" numbers between 2^62 and 2^63 (CAUTION: including 2^62 and excluding 2^63) first player (i.e. Louise) will be the "loser-even" player.

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In conclusion, for first, second and fourth inputs, output should be always "Richard".