문제<\/h2>
Two players are playing a game on a tape divided into cells that is infinite to the right. The cells are numbered with $1<\/mn>,<\/mo>2<\/mn>,<\/mo>3<\/mn>,<\/mo>\dots<\/mo><\/mrow>1, 2, 3, \ldots<\/math><\/span><\/span> 1<\/span>,<\/span> <\/span> 2<\/span>,<\/span> <\/span> 3<\/span>,<\/span> <\/span> \dots<\/span><\/span><\/span><\/span> from left to right. Each cell x<\/mi><\/mrow>x<\/math><\/span><\/span> x<\/span><\/span><\/span><\/span> is adjacent to cells x<\/mi>-<\/mo>1<\/mn><\/mrow>x - 1<\/math><\/span><\/span> x<\/span> <\/span> -<\/span> <\/span><\/span> <\/span> 1<\/span><\/span><\/span><\/span> and$

[이미지 1]<\/span><\/td>	[이미지 2]<\/span><\/td>	[이미지 3]<\/span><\/td> <\/tr>
Moving to an empty cell<\/td>	Moving to a cell with your own chips<\/td>	Moving to a cell with your opponent's chips<\/td> <\/tr> <\/tbody> <\/table> If both players run out of chips, the game ends in a draw. If only one player runs out of chips, they are declared the loser, and their opponent is declared the winner. Finally, if after $10<\/mn>100<\/mn><\/msup><\/mrow>10^{100}<\/math><\/span><\/span> 1<\/span> 0<\/span> <\/span> 100<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> turns the game has not ended, it is forcibly concluded and declared a draw.<\/p> You are given the initial setup of the tape. Determine who will win with perfect play from both players, and find any optimal first move for the first player.<\/p> 입력<\/h2> Each test contains multiple test cases. The first line contains the number of test cases t<\/mi><\/mrow>t<\/math><\/span><\/span> t<\/span><\/span><\/span><\/span> (1<\/mn>\leq<\/mo>t<\/mi>\leq<\/mo>10<\/mn>4<\/mn><\/msup><\/mrow>1 \le t \le 10^4<\/math><\/span><\/span> 1<\/span> <\/span> \leq<\/span> <\/span><\/span> <\/span>$

Game of Annihilation