How Many Balls?

문제

If a bag contains $rr$ red balls and $gg$ green balls and two balls are drawn at random, the probability of getting one ball of each color is $$P(r,g)=\frac{2rg}{(r+g)(r+g-1)}P(r,\; g)\; =\; \backslash frac\{2rg\}\{(r+g)(r\; +\; g\; -\; 1)\}$$

Write a program which takes as input a rational number $p\mathrm{/}qp/q$ in lowest terms and determines whether there is a number $r\le {10}^{6}r\; \backslash leq\; 10^6$ and a $g\ge rg\; \backslash geq\; r$ for which $P(r,g)=p\mathrm{/}qP(r,\; g)\; =\; p/q$.

입력

The only line of input contains two space-separated positive integers $pp$ ($p>0p\; >\; 0$) and $qq$ ($2p-1\le q\le 10002p\; -\; 1\; \backslash leq\; q\; \backslash leq\; 1000$). These two integers are guaranteed to be relatively prime.

출력

If there is a solution, print the two positive integers $rr$ and $gg$ satisfying the conditions above, separated by a space. If there are multiple solutions, output the one with the smallest $rr$ value. For any $rr$ value, there is at most one $gg$ value ($g\ge rg\; \backslash geq\; r$), which solves $P(r,g)=p\mathrm{/}qP(r,g)\; =\; p/q$. If there is no solution with $r\le {10}^{6}r\; \backslash leq\; 10^6$, print the word impossible.