Y by
Let
and
be positive integers. Kellem and Carmen play the following game: initially, the number
is on the board. Starting with Kellem and alternating turns, they add powers of
to the previous number on the board, such that the new value on the board does not exceed
. The player who writes
wins. Determine, for each pair
, who has the winning strategy.
Note: A power of
is a number of the form
, where
is a non-negative integer.







Note: A power of


