시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1.5 초 256 MB 69 28 14 53.846%

문제

철수는 혼자서 자연수 게임을 하고 있다. 자연수 게임을 하려면 파란 종이 한 장과 빨간 종이 한 장이 필요하다. 가장 처음에 두 종이에는 모두 1이 적혀있다.

게임은 두 종이 적힌 수의 합을 구하고, 그 값을 하나의 종이에 바꿔 적는 방식으로 진행된다. 이 과정 한 번을 "덧셈"이라고 부른다. "덧셈"을 반복해서 두 종이 중 하나에 철수가 원하는 수 x가 적히면 게임이 종료된다.

1보다 큰 정수 x에 대해서 게임을 할 때 계속 같은 색의 종이만 고른다면, 항상 x-1번의 덧셈 후에 게임이 끝난다. 철수는 x를 만드는 덧셈의 최소 횟수가 궁금해졌다. x가 주어졌을 때, 게임이 종료되는 덧셈의 최소 횟수를 구해보자.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 둘째 줄부터 T개의 줄에 x가 한 줄에 하나씩 주어진다.

출력

각각의 테스트 케이스마다 x를 만들기 위한 방법 중 덧셈 횟수가 최소인 것을 한 줄에 하나씩 출력한다.

x를 만드는 최소 덧셈 횟수가 M번인 경우에는 길이가 M인 문자열을 출력해야 하고, 파란 종이를 고른 것은 B, 빨간 종이를 고른 것은 R이다. 최소 덧셈 횟수를 만드는 방법이 여러가지인 경우에는 아무거나 출력한다.

제한

  • 1 ≤ T ≤ 100
  • 모든 테스트케이스의 x의 합은 20,000,000 이하이다.

서브태스크 1 (10점)

  • 1 ≤ x ≤ 500

서브태스크 2 (22점)

  • 1 ≤ x ≤ 300,000

예제 입력 1

4
2
3
4
5

예제 출력 1

B
RB
RRR
RBR

힌트

x = 5인 경우 아래와 같이 다양한 방법으로 5를 만들 수 있다. B는 파란 종이, R은 빨간 종이를 의미하고, 알파벳의 뒤에 적힌 수는 해당 종이에 적힌 수이다.

  • (B1, R1) → B를 선택 → (B2, R1) → R을 선택 → (B2, R3) → B를 선택 → (B5, R3) → 종료 (덧셈 3번)
  • (B1, R1) → B를 선택 → (B2, R1) → B를 선택 → (B3, R1) → B를 선택 → (B4, R1) → B를 선택 → (B5, R1) → 종료 (덧셈 4번)
[{"problem_id":"17431","problem_lang":"0","title":"\uac8c\uc784","description":"<p>\ucca0\uc218\ub294 \ud63c\uc790\uc11c \uc790\uc5f0\uc218 \uac8c\uc784\uc744 \ud558\uace0 \uc788\ub2e4. \uc790\uc5f0\uc218 \uac8c\uc784\uc744 \ud558\ub824\uba74 \ud30c\ub780 \uc885\uc774 \ud55c \uc7a5\uacfc \ube68\uac04 \uc885\uc774 \ud55c \uc7a5\uc774 \ud544\uc694\ud558\ub2e4. \uac00\uc7a5 \ucc98\uc74c\uc5d0&nbsp;\ub450 \uc885\uc774\uc5d0\ub294 \ubaa8\ub450 1\uc774 \uc801\ud600\uc788\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 \ub450 \uc885\uc774 \uc801\ud78c \uc218\uc758 \ud569\uc744 \uad6c\ud558\uace0, \uadf8 \uac12\uc744 \ud558\ub098\uc758 \uc885\uc774\uc5d0 \ubc14\uafd4 \uc801\ub294 \ubc29\uc2dd\uc73c\ub85c \uc9c4\ud589\ub41c\ub2e4. \uc774 \uacfc\uc815 \ud55c \ubc88\uc744 &quot;\ub367\uc148&quot;\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. &quot;\ub367\uc148&quot;\uc744 \ubc18\ubcf5\ud574\uc11c \ub450 \uc885\uc774 \uc911 \ud558\ub098\uc5d0 \ucca0\uc218\uac00 \uc6d0\ud558\ub294 \uc218 x\uac00 \uc801\ud788\uba74 \uac8c\uc784\uc774 \uc885\ub8cc\ub41c\ub2e4.<\/p>\r\n\r\n<p>1\ubcf4\ub2e4 \ud070 \uc815\uc218 x\uc5d0 \ub300\ud574\uc11c \uac8c\uc784\uc744 \ud560 \ub54c \uacc4\uc18d \uac19\uc740 \uc0c9\uc758 \uc885\uc774\ub9cc \uace0\ub978\ub2e4\uba74, \ud56d\uc0c1 x-1\ubc88\uc758 \ub367\uc148 \ud6c4\uc5d0 \uac8c\uc784\uc774 \ub05d\ub09c\ub2e4. \ucca0\uc218\ub294 x\ub97c \ub9cc\ub4dc\ub294 \ub367\uc148\uc758 \ucd5c\uc18c \ud69f\uc218\uac00 \uad81\uae08\ud574\uc84c\ub2e4. x\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uac8c\uc784\uc774 \uc885\ub8cc\ub418\ub294 \ub367\uc148\uc758 \ucd5c\uc18c \ud69f\uc218\ub97c \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\ubd80\ud130 T\uac1c\uc758 \uc904\uc5d0 x\uac00 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 x\ub97c \ub9cc\ub4e4\uae30 \uc704\ud55c \ubc29\ubc95 \uc911 \ub367\uc148 \ud69f\uc218\uac00 \ucd5c\uc18c\uc778 \uac83\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>x\ub97c \ub9cc\ub4dc\ub294 \ucd5c\uc18c \ub367\uc148 \ud69f\uc218\uac00 M\ubc88\uc778 \uacbd\uc6b0\uc5d0\ub294 \uae38\uc774\uac00 M\uc778 \ubb38\uc790\uc5f4\uc744 \ucd9c\ub825\ud574\uc57c \ud558\uace0, \ud30c\ub780 \uc885\uc774\ub97c \uace0\ub978 \uac83\uc740 B, \ube68\uac04 \uc885\uc774\ub97c \uace0\ub978 \uac83\uc740 R\uc774\ub2e4. \ucd5c\uc18c \ub367\uc148 \ud69f\uc218\ub97c \ub9cc\ub4dc\ub294 \ubc29\ubc95\uc774 \uc5ec\ub7ec\uac00\uc9c0\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>x = 5\uc778 \uacbd\uc6b0 \uc544\ub798\uc640 \uac19\uc774 \ub2e4\uc591\ud55c \ubc29\ubc95\uc73c\ub85c 5\ub97c \ub9cc\ub4e4 \uc218 \uc788\ub2e4. B\ub294 \ud30c\ub780 \uc885\uc774, R\uc740 \ube68\uac04 \uc885\uc774\ub97c \uc758\ubbf8\ud558\uace0, \uc54c\ud30c\ubcb3\uc758 \ub4a4\uc5d0 \uc801\ud78c \uc218\ub294 \ud574\ub2f9 \uc885\uc774\uc5d0 \uc801\ud78c \uc218\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>(B1, R1)&nbsp;&rarr; B\ub97c \uc120\ud0dd&nbsp;&rarr; (B2, R1)&nbsp;&rarr; R\uc744 \uc120\ud0dd&nbsp;&rarr; (B2, R3)&nbsp;&rarr; B\ub97c \uc120\ud0dd&nbsp;&rarr; (B5, R3)&nbsp;&rarr; \uc885\ub8cc (\ub367\uc148 3\ubc88)<\/li>\r\n\t<li>(B1, R1)&nbsp;&rarr; B\ub97c \uc120\ud0dd&nbsp;&rarr; (B2, R1)&nbsp;&rarr; B\ub97c \uc120\ud0dd&nbsp;&rarr; (B3, R1)&nbsp;&rarr; B\ub97c \uc120\ud0dd&nbsp;&rarr; (B4, R1)&nbsp;&rarr; B\ub97c \uc120\ud0dd &rarr; (B5, R1) &rarr; \uc885\ub8cc (\ub367\uc148 4\ubc88)<\/li>\r\n<\/ul>\r\n","original":"1","problem_lang_code":"\ud55c\uad6d\uc5b4","limit":"<ul>\r\n\t<li>1 &le; T &le; 100<\/li>\r\n\t<li>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 x\uc758 \ud569\uc740&nbsp;20,000,000 \uc774\ud558\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<ul>\r\n\t<li>1 &le; x &le; 500<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li>1 &le; x &le; 300,000<\/li>\r\n<\/ul>\r\n"},{"problem_id":"17431","problem_lang":"1","title":"Game","description":"<p>Albert is playing a game with numbers. To play the game, he needs two sheets&nbsp;of paper, one in blue and another in red. At first, both sheets have number &quot;1&quot; written on them.<\/p>\r\n\r\n<p>Albert plays the game as follows. First he calculates the sum of the two numbers written on the sheets. He then replaces the number on one of the sheets by this sum. One such move is called an &quot;addition&quot;. After applying addition(s), Albert ends the game when one of the sheets has x written on it (the number he initially chooses to play this game).<\/p>\r\n\r\n<p>For every integer x &gt; 1, if Albert chooses to write only on the same color sheet, then after (x-1) additions the game always ends. Albert wants to know the minimum number of additions he needs to perform in order to reach x.<\/p>\r\n","input":"<p>The first line will contain T, the number of test cases.<\/p>\r\n\r\n<p>Each of the next T lines will contain a single integer x.<\/p>\r\n","output":"<p>For each test case, you must output a string that describes how Albert can reach x with minimum number of additions.<\/p>\r\n\r\n<p>If M is the minimum number of additions Albert must do in order to get x, then the output must be a string of length M. Each character should be either B or R depending on which colored sheet Albert must write the summed number on. If there are multiple ways to achieve the minimum number of additions, you may output any one of them.<\/p>\r\n","hint":"<p>When x = 5, there are many ways to reach 5.<\/p>\r\n\r\n<p>B represents blue sheet and R represents red sheet. The number after B or R represents the number written on the respective sheet.<\/p>\r\n\r\n<ul>\r\n\t<li>(B1, R1) -&gt; Albert chooses B -&gt; (B2, R1) -&gt; Albert chooses R -&gt; (B2, R3) -&gt; Albert chooses B -&gt; (B5, R3) -&gt; Game ends (3 additions).<\/li>\r\n\t<li>(B1, R1) -&gt; Albert chooses B -&gt; (B2, R1) -&gt; Albert chooses B -&gt; (B3, R1) -&gt; Albert chooses B -&gt; (B4, R1) -&gt; Albert chooses B -&gt; (B5, R1) -&gt; Game ends (4 additions).<\/li>\r\n<\/ul>\r\n","original":"0","problem_lang_code":"\uc601\uc5b4","limit":"<ul>\r\n\t<li>1 &le; T &le; 100<\/li>\r\n\t<li>The sum of all x is at most 20,000,000.<\/li>\r\n<\/ul>\r\n","subtask1":"<ul>\r\n\t<li>1 &le; x &le; 500<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li>1 &le; x &le; 300,000<\/li>\r\n<\/ul>\r\n"}]

채점

  • 예제는 채점하지 않는다.