승기와 N-1명의 누나들은 크로아티아의 두브로브니크에서 여행을 하다가 길가의 한 카페에서 음료를 사먹었다. 음료의 총 가격은 A쿠나로 꽤 비쌌기 때문에 더치페이하기로 결정했다. 기본적으로 A쿠나를 1/N으로 나눠서 각 사람이 낸 후, 나이가 더 높은 누나들이 1쿠나씩 더 보탤 것이다.
예를 들어, N=5이고 A=13이면 승기와 4명의 누나들이 내는 돈은 각각 2쿠나, 2쿠나, 3쿠나, 3쿠나, 3쿠나 (승기가 가장 어리다)이다. 승기는 숙박시설 관리자와의 연락 문제로 돈을 먼저 냈다. 따라서 N-1명의 누나들이 내야 하는 돈은 총 B쿠나일 것이다. 음료의 총 가격은 승기밖에 모르고, 누나들은 B밖에 알 길이 없다. 누나들을 도와 음료의 총 가격을 구하는 프로그램을 작성하여라.
입력 예 1 2 5 출력 예 1 9 10 입력 예 2 3 5 출력 예 2 7 7
The youngest is sick and tired of just talking, so she conveniently decided to grab a hold of her share of the heritage. She knew exactly where her mother keeps her golden medallions . inside a thick sock in the third drawer next to the mirror in the hallway! The cunning daughter found this pile of medallions, split it into N equal parts, claimed her part and put the rest back into the sock. If the medallions couldn't have been split into N identical parts, then the parts were nearly identical: each differed from another by one medallion at most. In that case, the daughter claimed one of the smaller parts for herself.
The rest of the daughters found out about this (mis)deed so they counted the remaining medallions and now they want to know the initial number of medallions inside the sock, before the youngest one took her share. It is your task to answer this question. Given that there could be more than one possible answer, output both the smallest and the largest of them.
input 2 5 output 9 10 input 3 5 output 7 7 Clarification of the first example: There are two daughters, so that means the youngest daughter took half of the medallions. If there were initially 9 medallions, the youngest took 4, so 5 are remaining. If, by any chance, there were initially 10 medallions, she took 5 so there are also 5 remaining. Hence, the possible answers are both 9 and 10.
출처:coci/2013-2014/contest4 번역:functionx