문제
하볘는 Baekjoon Olympiad in Justification을 준비하고 있는 고등학생이다. 이를 위해 BOJ Archive에 있는 Project AtoZ의 Q번 문제를 풀려고 했으나, 문제가 생각보다 어려워서 풀지 못하고 있다.
Q번 문제는 다음과 같다.
0ドル$이 아닌 유리수 $x/y$에 대해 다음 조건을 만족하는 0ドル$이 아닌 4ドル$개의 정수 $a,ドル $b,ドル $c,ドル $d$가 존재함을 증명하시오.
- $\displaystyle \frac{a}{b} -\frac{c}{d} =\frac{a-c}{b-d} =\frac{x}{y}$.
이를 지켜보던 BOJ Archive의 랭커인 당신은 하볘를 도와주기로 했다. 하볘를 위해 유리수 $x/y$가 주어질 때 위 조건을 만족하는 $a,ドル $b,ドル $c,ドル $d$를 알려주는 프로그램을 만들어주자!
출력
각 테스트케이스에 대해, 문제의 조건을 만족하는 4ドル$개의 정수 $a,ドル $b,ドル $c,ドル $d$를 공백으로 구분하여 출력한다. $(1\le |a|,b,|c|,d<2^{63})$
$a$와 $c$는 음수가 될 수 있지만 $b$와 $d$는 음수가 될 수 없다는 점에 유의하라.
만약 가능한 답이 여러 가지라면 그중 아무거나 하나를 출력한다. 가능한 모든 입력에 대해 출력 조건을 만족하는 답이 있음을 보일 수 있다.
예제 출력 1
7 6 16 24
-408 12 17 2
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