문제
이 대회의 운영진 중 한 명인 KSA 학생은 얼마 전 소수 공포증을 극복했으나 또 다른 소수를 구별할 수 없게 되어 버렸다. KSA의 명예를 지키기 위해 어떤 소수 $k$를 입력받아 $k$를 나타내는 분수 $\cfrac{p}{q}$를 아무거나 구해주자.
$p$와 $q$는 10ドル^{9}$ 이하인 양의 정수이며, $k$와 $\cfrac{p}{q}$의 절대오차 또는 상대오차가 10ドル^{-6}$ 이하면 정답이다.
출력
첫 번째 줄에 조건을 만족하는 분수가 존재한다면 YES, 아니라면 NO를 출력한다.
만약 그러한 분수가 존재한다면, 두 번째 줄에 두 정수 $p,ドル $q$를 공백을 사이에 두고 출력한다.
정답이 여러 개 존재한다면 그중 아무거나 출력해도 상관없다.
제한
- 0ドル < k < 1$
- $k$는 최대 소수점 아래 여덟 자리까지 주어짐
- 소수 끝에 불필요한 0ドル$은 주어지지 않음
서브태스크
| 번호 | 배점 | 제한 | | 1 | 15 | $k$는 최대 소수점 한 자리까지 주어짐
|
| 2 | 85 | 추가 제약 조건 없음
|
노트
절대오차는 참값과 근삿값의 차이, 상대오차는 절대오차를 참값으로 나눈 값을 의미한다. 이 문제에서 참값은 $k$이고 근삿값은 $\cfrac{p}{q}$이다.
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