Mathematical Addition (Codeforces 1584A)
Tags: Math, math

Ivan decided to prepare for the test on solving integer equations. He noticed that all tasks in the test have the following form:  You are given two positive integers $$$u$$$ and $$$v$$$, find any pair of integers (not necessarily positive) $$$x$$$, $$$y$$$, such that: $$$$$$\frac{x}{u} + \frac{y}{v} = \frac{x + y}{u + v}.$$$$$$  The solution $$$x = 0$$$, $$$y = 0$$$ is forbidden, so you should find any solution with $$$(x, y) \neq (0, 0)$$$. Please help Ivan to solve some equations of this form.

Input: The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^3$$$) — the number of test cases. The next lines contain descriptions of test cases.The only line of each test case contains two integers $$$u$$$ and $$$v$$$ ($$$1 \leq u, v \leq 10^9$$$) — the parameters of the equation.

Output: For each test case print two integers $$$x$$$, $$$y$$$ — a possible solution to the equation. It should be satisfied that $$$-10^{18} \leq x, y \leq 10^{18}$$$ and $$$(x, y) \neq (0, 0)$$$.We can show that an answer always exists. If there are multiple possible solutions you can print any.

Note: In the first test case: $$$\frac{-1}{1} + \frac{1}{1} = 0 = \frac{-1 + 1}{1 + 1}$$$.In the second test case: $$$\frac{-4}{2} + \frac{9}{3} = 1 = \frac{-4 + 9}{2 + 3}$$$.In the third test case: $$$\frac{-18}{3} + \frac{50}{5} = 4 = \frac{-18 + 50}{3 + 5}$$$.In the fourth test case: $$$\frac{-4}{6} + \frac{9}{9} = \frac{1}{3} = \frac{-4 + 9}{6 + 9}$$$.

Sample Inputs:
4
1 1
2 3
3 5
6 9

Sample Outputs:
-1 1
-4 9
-18 50
-4 9

Solution (Python):
for s in [*open(0)][1:]:
    (u, v) = map(int, s.split())
    print(u * u, -v * v)

Solution (Python):
cases = int(input())
for i in range(cases):
    (x, y) = map(int, input().split())
    print(x * x * -1, y * y)

Solution (Python):
t = int(input())
r = []
for i in range(t):
    a = list(map(int, input().split()))
    u = a[0]
    v = a[1]
    res = []
    x = -u * u
    y = v * v
    res.append(x)
    res.append(y)
    r.append(' '.join(map(str, res)))
for i in range(len(r)):
    print(r[i])