시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 4 2 2 50.000%

문제

선영이는 계산기가 없으면 두 수의 나눗셈을 계산할 수 없다. 선영이는 다가오는 시험을 대비하기 위해 나눗셈을 계산해보려고 한다. 이번 시험에는 \(b\)진법으로 나타낸 두 수를 나눴을 때, 주기의 길이를 구하는 문제가 나온다. 선영이는 자신이 손으로 계산한 결과가 정답과 맞는지를 확인하는 프로그램을 작성하려고 한다.

진법 \(b\), 분자 \(x\), 분모 \(y\)가 주어진다. \(x\)와 \(y\)는 모두 \(b\)진법으로 나타낸 수이다. \(b\)진법 수 \(q = \frac {x} {y}\)의 주기를 구하는 프로그램을 작성하시오. 유리수 \(q\)를 b진법으로 나타내는 방법은 다음과 같다.

\(q=q_{n}q_{n-1}\dots q_{0}.q_{-1}q_{-2} \dots = \sum _{i=-\infty } ^{n}{q_ib^i}\)

아래는 예이다.

\(\frac {1_{10}}{2_{10}} = 0.5_{10}\), \(\frac {1_3} {10_3} = 0.1_3\), \(\frac {2_{10}}{11_{10}} = 0.181818\dots_{10} = 0.\overline { 18 }  _{10}\)

위의 처음 두 예제는 유한 소수이다. 따라서, 주기의 길이는 0이다. 첫 번째 예제의 경우에 주기의 길이가 1인 \(0.4\overline { 9 } _{ 10 }\)로 나타낼 수 있지만, 이 문제에서 그러한 경우는 신경쓰지 않는다.

세 번째 예제의 경우 주기의 길이는 2이다. 

입력

첫째 줄에 테스트 케이스의 수가 주어진다. 각 테스트 케이스는 한 줄로 이루어져 있으며, \(b\), \(x\), \(y\)가 주어진다. (2 ≤ \(b\) ≤ 36, 0 < \(y\) ≤ 10000010) 0부터 9까지 숫자로 나타낼 수 없는 자리는 'a'와 'A'로 시작하는 글자로 나타낸다. 이때, 대소문자는 구별하지 않는다. 

출력

각 테스트 케이스마다 "Scenario #i:"를 출력한 다음에, 주기의 길이를 출력한다. 각 테스트 케이스 사이에는 빈 칸을 하나 출력한다.

예제 입력 1

4
10 1 2
3 1 10
10 2 11
36 HI ho

예제 출력 1

Scenario #1:
0

Scenario #2:
0

Scenario #3:
2

Scenario #4:
13
[{"problem_id":"7546","problem_lang":"0","title":"\uc18c\uc218\uc758 \uc8fc\uae30","description":"<p>\uc120\uc601\uc774\ub294 \uacc4\uc0b0\uae30\uac00 \uc5c6\uc73c\uba74 \ub450 \uc218\uc758 \ub098\ub217\uc148\uc744 \uacc4\uc0b0\ud560 \uc218 \uc5c6\ub2e4. \uc120\uc601\uc774\ub294 \ub2e4\uac00\uc624\ub294 \uc2dc\ud5d8\uc744 \ub300\ube44\ud558\uae30 \uc704\ud574 \ub098\ub217\uc148\uc744 \uacc4\uc0b0\ud574\ubcf4\ub824\uace0 \ud55c\ub2e4. \uc774\ubc88 \uc2dc\ud5d8\uc5d0\ub294 \\(b\\)\uc9c4\ubc95\uc73c\ub85c \ub098\ud0c0\ub0b8 \ub450 \uc218\ub97c \ub098\ub234\uc744 \ub54c, \uc8fc\uae30\uc758 \uae38\uc774\ub97c \uad6c\ud558\ub294 \ubb38\uc81c\uac00 \ub098\uc628\ub2e4. \uc120\uc601\uc774\ub294 \uc790\uc2e0\uc774 \uc190\uc73c\ub85c \uacc4\uc0b0\ud55c \uacb0\uacfc\uac00 \uc815\ub2f5\uacfc \ub9de\ub294\uc9c0\ub97c \ud655\uc778\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc9c4\ubc95 \\(b\\), \ubd84\uc790 \\(x\\), \ubd84\ubaa8 \\(y\\)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \\(x\\)\uc640 \\(y\\)\ub294 \ubaa8\ub450 \\(b\\)\uc9c4\ubc95\uc73c\ub85c \ub098\ud0c0\ub0b8 \uc218\uc774\ub2e4. \\(b\\)\uc9c4\ubc95 \uc218 \\(q = \\frac {x} {y}\\)\uc758 \uc8fc\uae30\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc720\ub9ac\uc218 \\(q\\)\ub97c b\uc9c4\ubc95\uc73c\ub85c \ub098\ud0c0\ub0b4\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p>\\(q=q_{n}q_{n-1}\\dots q_{0}.q_{-1}q_{-2} \\dots = \\sum _{i=-\\infty } ^{n}{q_ib^i}\\)<\/p>\r\n\r\n<p>\uc544\ub798\ub294 \uc608\uc774\ub2e4.<\/p>\r\n\r\n<p>\\(\\frac {1_{10}}{2_{10}} = 0.5_{10}\\), \\(\\frac {1_3} {10_3} = 0.1_3\\), \\(\\frac {2_{10}}{11_{10}} = 0.181818\\dots_{10} = 0.\\overline { 18 } &nbsp;_{10}\\)<\/p>\r\n\r\n<p>\uc704\uc758 \ucc98\uc74c \ub450 \uc608\uc81c\ub294 \uc720\ud55c \uc18c\uc218\uc774\ub2e4. \ub530\ub77c\uc11c, \uc8fc\uae30\uc758 \uae38\uc774\ub294 0\uc774\ub2e4. \uccab \ubc88\uc9f8 \uc608\uc81c\uc758 \uacbd\uc6b0\uc5d0 \uc8fc\uae30\uc758 \uae38\uc774\uac00 1\uc778 \\(0.4\\overline { 9 } _{ 10 }\\)\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uc9c0\ub9cc, \uc774 \ubb38\uc81c\uc5d0\uc11c \uadf8\ub7ec\ud55c \uacbd\uc6b0\ub294 \uc2e0\uacbd\uc4f0\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \uc608\uc81c\uc758 \uacbd\uc6b0 \uc8fc\uae30\uc758 \uae38\uc774\ub294 2\uc774\ub2e4.&nbsp;<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \\(b\\), \\(x\\), \\(y\\)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; \\(b\\) &le; 36, 0 &lt; \\(y\\) &le; 100000<sub>10<\/sub>) 0\ubd80\ud130 9\uae4c\uc9c0 \uc22b\uc790\ub85c \ub098\ud0c0\ub0bc \uc218 \uc5c6\ub294 \uc790\ub9ac\ub294 &#39;a&#39;\uc640 &#39;A&#39;\ub85c \uc2dc\uc791\ud558\ub294 \uae00\uc790\ub85c \ub098\ud0c0\ub0b8\ub2e4. \uc774\ub54c, \ub300\uc18c\ubb38\uc790\ub294 \uad6c\ubcc4\ud558\uc9c0 \uc54a\ub294\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 &quot;Scenario #i:&quot;\ub97c \ucd9c\ub825\ud55c \ub2e4\uc74c\uc5d0, \uc8fc\uae30\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \uc0ac\uc774\uc5d0\ub294 \ube48 \uce78\uc744 \ud558\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"7546","problem_lang":"1","title":"Extra Terrestrial PISA Test","description":"<p>On the planet Divido teachers have a serious problem. Due to the spread of calculators the students cannot do long division with pencil and paper any longer. But now the planetarian government has announced a test for all students in basic schools to test their math skills. Because it has to be a multiple choice test the students only have to calculate the length of the period when dividing two numbers. Your task is to write a program which calculates the right solutions in advance to ease the correction of the test. An additional problem occurs because not all intelligent species on Divido have the same number of \ufb01ngers and thus their systems of numbers have different bases.<\/p>\r\n\r\n<p>You are given a base \\(b\\), a numerator \\(x\\), and a denominator \\(y\\), the latter of which are integers to the base \\(b\\). Then calculate the length of the period in the base \\(b\\) expansion of the fraction \\(q = \\frac{x}{y}\\). Remember that the digits of the base \\(b\\) expansion of the the rational number \\(q\\) are the coef\ufb01cients of the powers of the base:<\/p>\r\n\r\n<p>\\(q=q_{n}q_{n-1}\\dots q_{0}.q_{-1}q_{-2} \\dots = \\sum _{i=-\\infty } ^{n}{q_ib^i}\\)<\/p>\r\n\r\n<p>Here are some examples:<\/p>\r\n\r\n<p>\\(\\frac {1_{10}}{2_{10}} = 0.5_{10}\\), \\(\\frac {1_3} {10_3} = 0.1_3\\), \\(\\frac {2_{10}}{11_{10}} = 0.181818\\dots_{10} = 0.\\overline { 18 } &nbsp;_{10}\\)<\/p>\r\n\r\n<p>In the \ufb01rst two examples, there is a \ufb01nite base \\(b\\) expansion of the fraction, meaning that all digits that follow are zero. In that case, we say that the length of the period is zero. Note that one could as well express the \ufb01rst example as \\(0.4\\overline { 9 } _{ 10 }\\) with a period length of one, but that is not what we want.<\/p>\r\n\r\n<p>In the third example, however, the period length is unambiguously two.<\/p>\r\n","input":"<p>The \ufb01rst line contains the number of fractions. For each fraction you are \ufb01rst given the base \\(b\\) as a decimal number with 2 &le; \\(b\\) &le; 36, and then the numerator \\(x\\) and the denominator \\(y\\) of the fraction to that base separated by single blanks. It is guaranteed that the denominator satis\ufb01es 0 &lt; \\(y\\) &le; 100 000<sub>10<\/sub>. Digits not in the range of 0...9 are represented by letters starting from &ldquo;a&rdquo; or &ldquo;A&rdquo; in the usual way, where case does not matter.<\/p>\r\n","output":"<p>The output for every scenario begins with a line containing &ldquo;Scenario #i:&rdquo;, where i is the number of the scenario starting at 1. Then print a single line containing the length of the period in the base \\(b\\) expansion of \\(\\frac{x}{y}\\) , but make sure to print the length as a decimal number. Terminate the output for the scenario with a blank line.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_code":"\uc601\uc5b4"}]