시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 256 MB69611180401350526.629%

문제

최근에 ICPC 탐사대는 남아메리카의 잉카 제국이 놀라운 문명을 지닌 카잉 제국을 토대로 하여 세워졌다는 사실을 발견했다. 카잉 제국의 백성들은 특이한 달력을 사용한 것으로 알려져 있다. 그들은 M과 N보다 작거나 같은 두 개의 자연수 x, y를 가지고 각 년도를 <x:y>와 같은 형식으로 표현하였다. 그들은 이 세상의 시초에 해당하는 첫 번째 해를 <1:1>로 표현하고, 두 번째 해를 <2:2>로 표현하였다. <x:y>의 다음 해를 표현한 것을 <x':y'>이라고 하자. 만일 x < M 이면 x' = x + 1이고, 그렇지 않으면 x' = 1이다. 같은 방식으로 만일 y < N이면 y' = y + 1이고, 그렇지 않으면 y' = 1이다. <M:N>은 그들 달력의 마지막 해로서, 이 해에 세상의 종말이 도래한다는 예언이 전해 온다.

예를 들어, M = 10 이고 N = 12라고 하자. 첫 번째 해는 <1:1>로 표현되고, 11번째 해는 <1:11>로 표현된다. <3:1>은 13번째 해를 나타내고, <10:12>는 마지막인 60번째 해를 나타낸다.

네 개의 정수 M, N, x와 y가 주어질 때, <M:N>이 카잉 달력의 마지막 해라고 하면 <x:y>는 몇 번째 해를 나타내는지 구하는 프로그램을 작성하라.

입력

입력 데이터는 표준 입력을 사용한다. 입력은 T개의 테스트 데이터로 구성된다. 입력의 첫 번째 줄에는 입력 데이터의 수를 나타내는 정수 T가 주어진다. 각 테스트 데이터는 한 줄로 구성된다. 각 줄에는 네 개의 정수 M, N, x와 y가 주어진다. (1 ≤ M, N ≤ 40,000, 1 ≤ x ≤ M, 1 ≤ y ≤ N) 여기서 <M:N>은 카잉 달력의 마지막 해를 나타낸다.

출력

출력은 표준 출력을 사용한다. 각 테스트 데이터에 대해, 정수 k를 한 줄에 출력한다. 여기서 k는 <x:y>가 k번째 해를 나타내는 것을 의미한다. 만일 <x:y>에 의해 표현되는 해가 없다면, 즉, <x:y>가 유효하지 않은 표현이면, -1을 출력한다.

예제 입력 1

3
10 12 3 9
10 12 7 2
13 11 5 6

예제 출력 1

33
-1
83
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(1 &le; M, N &le; 40,000, 1 &le; x &le; M, 1 &le; y &le; N) \uc5ec\uae30\uc11c &lt;M:N&gt;\uc740 \uce74\uc789 \ub2ec\ub825\uc758 \ub9c8\uc9c0\ub9c9 \ud574\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900 \ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\uc5d0 \ub300\ud574, \uc815\uc218 k\ub97c \ud55c \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4. \uc5ec\uae30\uc11c k\ub294 &lt;x:y&gt;\uac00 k\ubc88\uc9f8 \ud574\ub97c \ub098\ud0c0\ub0b4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. \ub9cc\uc77c &lt;x:y&gt;\uc5d0 \uc758\ud574 \ud45c\ud604\ub418\ub294 \ud574\uac00 \uc5c6\ub2e4\uba74, \uc989, &lt;x:y&gt;\uac00 \uc720\ud6a8\ud558\uc9c0 \uc54a\uc740 \ud45c\ud604\uc774\uba74, -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"6064","problem_lang":"1","title":"Cain Calendar","description":"<p>It was recently revealed by the ICPC excavation team that the Inca Empire was established just after the Cain Empire which was a splendid civilization that flourished in South America. It is believed that the people in the Cain Empire used an interesting odd calendar. In their calendar, a year was represented by &lt;x:y&gt;, where x and y are natural numbers which are less than or equal to M and N, respectively. The first year, that is, the beginning of the world is represented by &lt;1:1&gt;. The second year is represented by &lt;2:2&gt;. Let &lt;x&#39;:y&#39;&gt;be the following year of &lt;x:y&gt;. If x &lt; M, x&#39; = x + 1, otherwise x&#39; = 1. Similarly, if y &lt; N, y&#39; = y + 1, otherwise y&#39; = 1. The last year of their calendar is &lt;M:N&gt;. It is said that there was a prophecy which states the world ends in the year &lt;M:N&gt;.&nbsp;<\/p>\r\n\r\n<p>For example, assume that M = 10 and N = 12. The first year is represented by &lt;1:1&gt;. The year &lt;1:11&gt; represents the 11<sup>th<\/sup> year, &lt;3:1&gt; represents the 13<sup>th<\/sup> year, and &lt;10:12&gt; represents the 60<sup>th<\/sup> year which is the last year.&nbsp;<\/p>\r\n\r\n<p>Given four integers M, N, x, and y, write a program that computes the number k such that &lt;x:y&gt; represents the k<sup>th<\/sup> year, where &lt;x:y&gt; is the last year of the world in the Cain Calendar.<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case consists of a single line containing four integers M, N, x, and y (1 &le; M,N &le; 40 000, 1 &le; x &le; M, 1 &le; y &le; N), where &lt;M:N&gt; is the last year of the world in the Cain Calendar.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain an integer k, where the k<sup>th<\/sup> year is represented by &lt;x:y&gt; for x and y given in the input. If there doesn&rsquo;t exist a year represented by &lt;x:y&gt;, print -1.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Korea > Nationwide Internet Competition > Daejeon Nationalwide Internet Competition 2013 B번