시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 88 9 5 9.259%

문제

6과 9를 곱하면 몇이 될까? 정답은 42이다. 54로 생각했다면, 잠시 쉬었다가 문제를 푸는 것을 권장한다. 그 이유는 42는 13진법으로 계산했을 때 결과이기 때문이다.

2보다 크거나 같은 정수 B에 대해서, B진법의 모든 자리수는 0보다 크거나 같고, B-1보다 작거나 같은 정수이다. B진법 수를 읽으려면 가장 오른쪽 자리에 1을 곱하고, 두 번째 오른쪽 자리에 B를 곱하고, 세 번째 오른쪽 자리에 B2를 곱하고, ... 이와 같은 식으로 계속 곱해야 한다.

일부 등식은 어떤 진법을 사용했냐에 따라서 참과 거짓이 결정된다. 예를 들어, 2+2=4의 경우에 B≥5이면 항상 참이다. 4진법에는 4를 자리로 사용할 수 없기 때문에 B≥5이다. 하지만, 2+2=5와 같은 등식은 어떤 진법을 사용해도 참이 될 수 없다.

등식이 주어졌을 때, 어떤 진법을 사용하면 참이 되는지 구하는 프로그램을 작성하시오. 

입력

입력의 각 줄은 테스트 케이스 하나를 나타내며, 각 테스트 케이스는 "EXPR=EXPR"과 같은 형태이다. EXPR는 17자리를 넘지 않는 수식이다.

모든 수식은 항상 올바르며, '+', '*'와 '0'-'9'까지 숫자로 이루어져 있다. 수식이 '+'기호로 시작하는 경우는 없으며, 수의 앞에 불필요한 0이 붙어있는 경우도 없다.

입력의 마지막 줄에는 '='이 주어진다.

출력

각 테스트 케이스마다 어떤 진법을 사용하면 입력으로 주어진 등식이 참이 되는지 출력한다.

등식을 참으로 만드는 진법이 무한대인 경우에는 "B+"를 출력한다. 여기서 B는 등식을 참으로 만드는 가장 작은 진법이다.

진법의 수가 유한개인 경우에는 진법을 오름차순으로 공백으로 구분하여 출력한다.

어떤 진법을 사용해도 등식이 참이 되지 않는 경우에는 '*'을 출력한다.

예제 입력 1

6*9=42
10000+3*5*334=3*5000+10+0
2+2=3
2+2=4
0*0=0
=

예제 출력 1

13
6 10
*
5+
2+
[{"problem_id":"5720","problem_lang":"0","title":"\uc9c4\ubc95 \uc54c\uc544\ub0b4\uae30","description":"<p>6\uacfc 9\ub97c \uacf1\ud558\uba74 \uba87\uc774 \ub420\uae4c? \uc815\ub2f5\uc740 42\uc774\ub2e4. 54\ub85c \uc0dd\uac01\ud588\ub2e4\uba74, \uc7a0\uc2dc \uc26c\uc5c8\ub2e4\uac00 \ubb38\uc81c\ub97c \ud478\ub294 \uac83\uc744 \uad8c\uc7a5\ud55c\ub2e4. \uadf8 \uc774\uc720\ub294 42\ub294 13\uc9c4\ubc95\uc73c\ub85c \uacc4\uc0b0\ud588\uc744 \ub54c \uacb0\uacfc\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\r\n\r\n<p>2\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uc740 \uc815\uc218 B\uc5d0 \ub300\ud574\uc11c, B\uc9c4\ubc95\uc758 \ubaa8\ub4e0 \uc790\ub9ac\uc218\ub294 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, B-1\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218\uc774\ub2e4. B\uc9c4\ubc95 \uc218\ub97c \uc77d\uc73c\ub824\uba74 \uac00\uc7a5 \uc624\ub978\ucabd \uc790\ub9ac\uc5d0 1\uc744 \uacf1\ud558\uace0, \ub450 \ubc88\uc9f8 \uc624\ub978\ucabd \uc790\ub9ac\uc5d0 B\ub97c \uacf1\ud558\uace0, \uc138 \ubc88\uc9f8 \uc624\ub978\ucabd \uc790\ub9ac\uc5d0 B<sup>2<\/sup>\ub97c \uacf1\ud558\uace0, ... \uc774\uc640 \uac19\uc740 \uc2dd\uc73c\ub85c \uacc4\uc18d \uacf1\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc77c\ubd80 \ub4f1\uc2dd\uc740 \uc5b4\ub5a4 \uc9c4\ubc95\uc744 \uc0ac\uc6a9\ud588\ub0d0\uc5d0 \ub530\ub77c\uc11c \ucc38\uacfc \uac70\uc9d3\uc774&nbsp;\uacb0\uc815\ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 2+2=4\uc758 \uacbd\uc6b0\uc5d0 B&ge;5\uc774\uba74 \ud56d\uc0c1 \ucc38\uc774\ub2e4. 4\uc9c4\ubc95\uc5d0\ub294 4\ub97c \uc790\ub9ac\ub85c \uc0ac\uc6a9\ud560 \uc218 \uc5c6\uae30 \ub54c\ubb38\uc5d0 B&ge;5\uc774\ub2e4. \ud558\uc9c0\ub9cc, 2+2=5\uc640 \uac19\uc740 \ub4f1\uc2dd\uc740 \uc5b4\ub5a4 \uc9c4\ubc95\uc744 \uc0ac\uc6a9\ud574\ub3c4 \ucc38\uc774 \ub420 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ub4f1\uc2dd\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc5b4\ub5a4 \uc9c4\ubc95\uc744 \uc0ac\uc6a9\ud558\uba74 \ucc38\uc774 \ub418\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.&nbsp;<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uac01 \uc904\uc740 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ud558\ub098\ub97c \ub098\ud0c0\ub0b4\uba70, \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 &quot;EXPR=EXPR&quot;\uacfc \uac19\uc740 \ud615\ud0dc\uc774\ub2e4. EXPR\ub294 17\uc790\ub9ac\ub97c \ub118\uc9c0 \uc54a\ub294 \uc218\uc2dd\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc218\uc2dd\uc740 \ud56d\uc0c1 \uc62c\ubc14\ub974\uba70, &#39;+&#39;, &#39;*&#39;\uc640 &#39;0&#39;-&#39;9&#39;\uae4c\uc9c0 \uc22b\uc790\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uc218\uc2dd\uc774 &#39;+&#39;\uae30\ud638\ub85c \uc2dc\uc791\ud558\ub294 \uacbd\uc6b0\ub294 \uc5c6\uc73c\uba70, \uc218\uc758 \uc55e\uc5d0 \ubd88\ud544\uc694\ud55c 0\uc774 \ubd99\uc5b4\uc788\ub294 \uacbd\uc6b0\ub3c4 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 &#39;=&#39;\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uc5b4\ub5a4 \uc9c4\ubc95\uc744 \uc0ac\uc6a9\ud558\uba74 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ub4f1\uc2dd\uc774 \ucc38\uc774 \ub418\ub294\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub4f1\uc2dd\uc744 \ucc38\uc73c\ub85c \ub9cc\ub4dc\ub294 \uc9c4\ubc95\uc774 \ubb34\ud55c\ub300\uc778 \uacbd\uc6b0\uc5d0\ub294 &quot;B+&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc5ec\uae30\uc11c B\ub294 \ub4f1\uc2dd\uc744 \ucc38\uc73c\ub85c \ub9cc\ub4dc\ub294 \uac00\uc7a5 \uc791\uc740 \uc9c4\ubc95\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc9c4\ubc95\uc758 \uc218\uac00 \uc720\ud55c\uac1c\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc9c4\ubc95\uc744 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \uc9c4\ubc95\uc744 \uc0ac\uc6a9\ud574\ub3c4 \ub4f1\uc2dd\uc774 \ucc38\uc774 \ub418\uc9c0 \uc54a\ub294 \uacbd\uc6b0\uc5d0\ub294 &#39;*&#39;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5720","problem_lang":"1","title":"Bases","description":"<p>What do you get if you multiply 6 by 9? The answer, of course, is 42, but only if you do the calculations in base 13.<\/p>\r\n\r\n<p>Given an integer B &ge; 2, the base B numbering system is a manner of writing integers using only digits between 0 and B &minus; 1, inclusive. In a number written in base B, the rightmost digit has its value multiplied by 1, the second rightmost digit has its value multiplied by B, the third rightmost digit has its value multiplied by B<sup>2<\/sup>, and so on.<\/p>\r\n\r\n<p>Some equations are true or false depending on the base they are considered in. The equation 2 + 2 = 4, for instance, is true for any B &ge; 5 &mdash; it does not hold in base 4, for instance, sincethere is no digit &lsquo;4&rsquo; in base 4. On the other hand, an equation like 2 + 2 = 5 is never true.<\/p>\r\n\r\n<p>Write a program that given an equation determines for which bases it holds.<\/p>\r\n","input":"<p>Each line of the input contains a test case; each test case is an equation of the form &ldquo;EXPR=EXPR&rdquo;, where both &ldquo;EXPR&rdquo; are arithmetic expressions with at most 17 characters.<\/p>\r\n\r\n<p>All expressions are valid, and contain only the characters &lsquo;+&rsquo;, &lsquo;*&rsquo; and the digits from &lsquo;0&rsquo; to &lsquo;9&rsquo;. No expressions contain leading plus signs, and no numbers in it have leading zeros.<\/p>\r\n\r\n<p>The end of input is indicated by a line containing only &ldquo;=&rdquo;.<\/p>\r\n","output":"<p>For each test case in the input your program should produce a single line in the output, indicating for which bases the given equation holds.<\/p>\r\n\r\n<p>If the expression is true for in\ufb01nitely many bases, print &ldquo;B+&rdquo;, where B is the \ufb01rst base for which the equation holds.<\/p>\r\n\r\n<p>If the expression is valid only for a \ufb01nite set of bases, print them in ascending order, separated by single spaces.<\/p>\r\n\r\n<p>If the expression is not true in any base, print the character &lsquo;*&rsquo;.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ICPC > Regionals > Latin America > South America Regional Contests 2008 B번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: lsh0426