After participating in the MFP (Matchup of Finalists in Ping-pong) in Campinas, Giovana and Julia are tired of playing ping-pong and decide they need to devise a new sport. They want a sport that, besides physical performance, requires mathematical reasoning and strategy. As both are very fond of binary numbers, they thought of the following game, which they named "Bit Tennis", to play against each other:

• The game starts with a string $$$S$$$, of size $$$N$$$, that represents a number in binary;
• Giovana begins the game and thereafter they alternate turns between Julia and her;
• In each round, the current player can add one more digit ("0" or "1") to the end or the beginning of the string: for example, if the string is "110", the player can turn it into "1100", "1101", "0110" or "1110".
• If, after $$$K$$$ turns from each player, the number is a multiple of 3, Julia wins. Otherwise, Giovana wins.

Both quickly learned to play optimally and, after playing a few times, they noticed that the game's outcome is always determined before the first move is even made. Curious about this fact, they asked for your help to, given the initial string and number of turns, find out which one of them will win.