题目描述

For a positive integer $s$, you can perform the following operation an arbitrary number of times (including zero): Choose a positive integer triplet $(a, b, c)$ such that $s \in \{a, b, c\}$, $a^2 + b^2 = c^2$. Choose a positive integer $t \in \{a, b, c\}\setminus \{s\}$,then replace $s$ with $t$. Given $S$ and $T$, you need to transform $S$ into $T$ within 2000 steps ensuring that the value of each number during the transformation does not exceed or determine that it is not possible.官方中文

输入格式

The only line of input contains two integers $S,T$ $(1\leq S,T\leq 10^9, S\neq T)$.官方中文

输出格式

If it is not possible to transform $S$ into $T$ within 2000 steps, output “impossible” in a line. The first line contains one integer $m$ $(1\leq m\leq 2000)$, denoting the number of steps. Then you need to output $m$ lines, with the $i$-th line containing a positive integer $x$ $(1\leq x\leq 10^{18})$, representing the result after the $i$-th operation.官方中文