시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 75 4 4 7.547%

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 거짓일 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 없으면, 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+
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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. 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