Pythagorathean Transformation

时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 1024 M，其他语言2048 M
Special Judge, 64bit IO Format: %lld

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 $10^{18}$ or determine that it is not possible.

输入描述:

The only line of input contains two integers  .

输出描述:

If it is not possible to transform  into  within 2000 steps, output “impossible” in a line.

The first line contains one integer  , denoting the number of steps.

Then you need to output  lines, with the -th line containing a positive integer  , representing the result after the -th operation.

示例1

输入

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3 5

输出

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1
5

示例2

输入

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4 12

输出

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2
5
12

示例3

输入

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1 100

输出

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impossible