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#10903. 奇怪的分数

الإحصائيات

给定一个正分数 $\frac{p}{q}$,你需要找到两个正整数 $a, b$,使得 $\frac{p}{q} = \frac{a}{b} + \frac{b}{a}$。如果不存在这样的整数,请报告。

输入格式

第一行包含一个整数 $T$ ($1 \le T \le 10^5$),表示测试用例的数量。

对于每个测试用例: 输入一行,包含两个整数 $p, q$ ($1 \le p, q \le 10^7$),表示给定的分数。

输出格式

对于每个测试用例: 如果存在解,输出一行,包含两个整数 $a, b$ ($1 \le a, b \le 10^9$);如果不存在解,则输出一行两个零。

样例

样例输入 1

2
5 2
5 1

样例输出 1

1 2
0 0

说明

对于第一个样例,$\frac{5}{2} = \frac{1}{2} + \frac{2}{1}$ 成立。因此一个可能的解是 $a = 1, b = 2$。

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