Giovana and Julia, after becoming the champions of the Bit Tennis doubles tournament on Earth, decided to travel to another planet in search of more competition. During the trip, they remembered they had a holographic piece board that allows them to play various games. Since they were already bored of all the games (including Bit Tennis), they decided to invent a new game: Bit Tennis 2.

The rules of the game are as follows:

• The game starts with $$$N$$$ stacks of holographic pieces, where the $$$i$$$-th stack contains $$$a_i$$$ pieces;
• Julia starts the game, and after that, the turns alternate between Giovana and Julia;
• On each turn, the player must choose a stack and remove any number of pieces that is a power of 2;
• The player who cannot make a move loses the game.

For the game with stack sizes [5, 1, 3, 2], Julia, by starting, has a strategy that ensures Giovana cannot win the game.

They both realized that the game was very difficult for the second player, so they added a new rule: before the game begins, Giovana must perform the following operation exactly $$$X$$$ times:

• Choose a stack and double the number of pieces in it. That is, if Giovana chooses stack $$$i$$$, which has $$$a_i$$$ pieces, it now has $$$2 \cdot a_i$$$ pieces.

Both players, just like when they invented Bit Tennis, quickly learned to play optimally and noticed that the outcome of the game seems to be determined even before the first move is made. Curious about this fact, they asked for your help. Given $$$N$$$, $$$X$$$, and the size of each stack, they ask you to determine who will be the winner.