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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 M 과 N 보다 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, 11 번째 해는 <1:11>로 표현된다. <3:1>은 13 번째 해를 나타내고, <10:12>는 마지막인 60 번째 해를 나타낸다. 

네 개의 정수 M, N, x 와 y가 주어질 때, <M:N>이 카잉 달력의 마지막 해라고 하면 <x:y>는 몇 번째 해를 나타내는 지를 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

힌트

[{"problem_id":"6064","problem_lang":"0","title":"\uce74\uc789 \ub2ec\ub825","description":"<p>\ucd5c\uadfc\uc5d0 ICPC \ud0d0\uc0ac\ub300\ub294 \ub0a8\uc544\uba54\ub9ac\uce74\uc758 \uc789\uce74 \uc81c\uad6d\uc774 \ub180\ub77c\uc6b4 \ubb38\uba85\uc744 \uc9c0\ub2cc \uce74\uc789 \uc81c\uad6d\uc744 \ud1a0\ub300\ub85c \ud558\uc5ec \uc138\uc6cc\uc84c\ub2e4\ub294 \uc0ac\uc2e4\uc744 \ubc1c\uacac\ud588\ub2e4. \uce74\uc789 \uc81c\uad6d\uc758 \ubc31\uc131\ub4e4\uc740 \ud2b9\uc774\ud55c \ub2ec\ub825\uc744 \uc0ac\uc6a9\ud55c \uac83\uc73c\ub85c \uc54c\ub824\uc838 \uc788\ub2e4. \uadf8\ub4e4\uc740 M \uacfc N \ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \ub450 \uac1c\uc758 \uc790\uc5f0\uc218 x, y\ub97c \uac00\uc9c0\uace0 \uac01 \ub144\ub3c4\ub97c &lt;x:y&gt;\uc640 \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \ud45c\ud604\ud558\uc600\ub2e4. \uadf8\ub4e4\uc740 \uc774 \uc138\uc0c1\uc758 \uc2dc\ucd08\uc5d0 \ud574\ub2f9\ud558\ub294 \uccab \ubc88\uc9f8 \ud574\ub97c &lt;1:1&gt;\ub85c \ud45c\ud604\ud558\uace0, \ub450 \ubc88\uc9f8 \ud574\ub97c &lt;2:2&gt;\ub85c \ud45c\ud604\ud558\uc600\ub2e4. &lt;x:y&gt;\uc758 \ub2e4\uc74c \ud574\ub97c \ud45c\ud604\ud55c \uac83\uc744 &lt;x&#39;:y&#39;&gt;\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc77c x&nbsp;&lt; M \uc774\uba74 x&#39; = x + 1\uc774\uace0, \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74 x&#39; = 1\uc774\ub2e4. \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \ub9cc\uc77c y &lt; N\uc774\uba74 y&#39; = y + 1\uc774\uace0, \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74 y&#39; = 1\uc774\ub2e4. &lt;M:N&gt;\uc740 \uadf8\ub4e4 \ub2ec\ub825\uc758 \ub9c8\uc9c0\ub9c9 \ud574\ub85c\uc11c, \uc774 \ud574\uc5d0 \uc138\uc0c1\uc758 \uc885\ub9d0\uc774 \ub3c4\ub798\ud55c\ub2e4\ub294 \uc608\uc5b8\uc774 \uc804\ud574 \uc628\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, M = 10 \uc774\uace0 N = 12\ub77c\uace0 \ud558\uc790. \uccab \ubc88\uc9f8 \ud574\ub294 &lt;1:1&gt;\ub85c \ud45c\ud604\ub418\uace0, 11 \ubc88\uc9f8 \ud574\ub294 &lt;1:11&gt;\ub85c \ud45c\ud604\ub41c\ub2e4. &lt;3:1&gt;\uc740 13 \ubc88\uc9f8 \ud574\ub97c \ub098\ud0c0\ub0b4\uace0, &lt;10:12&gt;\ub294 \ub9c8\uc9c0\ub9c9\uc778 60 \ubc88\uc9f8 \ud574\ub97c \ub098\ud0c0\ub0b8\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ub124 \uac1c\uc758 \uc815\uc218 M, N, x \uc640 y\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, &lt;M:N&gt;\uc774 \uce74\uc789 \ub2ec\ub825\uc758 \ub9c8\uc9c0\ub9c9 \ud574\ub77c\uace0 \ud558\uba74 &lt;x:y&gt;\ub294 \uba87 \ubc88\uc9f8 \ud574\ub97c \ub098\ud0c0\ub0b4\ub294 \uc9c0\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c.&nbsp;<\/p>\r\n","input":"<p>\uc785\ub825&nbsp;\ub370\uc774\ud130\ub294 \ud45c\uc900 \uc785\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc785\ub825\uc740 T\uac1c\uc758 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\ub85c \uad6c\uc131\ub41c\ub2e4. \uc785\ub825\uc758 \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc785\ub825 \ub370\uc774\ud130\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\ub294 \ud55c \uc904\ub85c \uad6c\uc131\ub41c\ub2e4. \uac01 \uc904\uc5d0\ub294 \ub124 \uac1c\uc758 \uc815\uc218 M, N, x\uc640 y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (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","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"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","problem_lang_code":"\uc601\uc5b4"}]