D. Umka and a Long Flighttime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe girl Umka loves to travel and participate in math olympiads. One day she was flying by plane to the next olympiad and out of boredom explored a huge checkered sheet of paper.Denote the n-th Fibonacci number as F_n = \begin{cases} 1, & n = 0; \\ 1, & n = 1; \\ F_{n-2} + F_{n-1}, & n \ge 2. \end{cases}A checkered rectangle with a height of F_n and a width of F_{n+1} is called a Fibonacci rectangle of order n.Umka has a Fibonacci rectangle of order n. Someone colored a cell in it at the intersection of the row x and the column y.It is necessary to cut this rectangle exactly into n+1 squares in such way that  the painted cell was in a square with a side of 1;  there was at most one pair of squares with equal sides;  the side of each square was equal to a Fibonacci number. Will Umka be able to cut this rectangle in that way?InputThe first line contains an integer t (1 \le t \le 2 \cdot 10^5) — number of test cases.For each test case the integers n, x, y are given (1 \le n \le 44, 1 \le x \le F_n, 1 \le y \le F_{n+1}) — the order of the Fibonacci rectangle and the coordinates of the colored cell.OutputFor each test case, print "YES" if the answer is positive, and "NO" otherwise.You can print "YES" and "NO" in any case (for example, the strings "yEs", "yes" and "Yes" will be recognized as a positive answer).ExampleInput
121 1 12 1 23 1 43 3 24 4 64 3 35 6 55 4 125 2 124 2 11 1 244 758465880 1277583853Output
YES
NO
YES
YES
YES
NO
YES
NO
NO
YES
YES
NO
Note  The first, third and fourth test cases. 
121 1 12 1 23 1 43 3 24 4 64 3 35 6 55 4 125 2 124 2 11 1 244 758465880 1277583853
YES NO YES YES YES NO YES NO NO YES YES NO 
['constructive algorithms', 'implementation', 'math', '*1600']