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문제

만칼라는 보드 게임의 한 종류로, 여러 변형 판이 존재한다.

그 중 가장 간단한 종류인 1인용 만칼라 게임 Tchoukaillon에 대해 살펴볼 것이다.

Tchoukaillon는 여러 개의 빈칸과 하나의 Roumba로 이루어진 보드 위에서 진행된다.

가장 왼쪽의 빈칸은 Roumba이며, 처음엔 항상 비어있는 상태여야 한다.

게임은 다음과 같이 진행된다. 우선, 각 칸을 B[N]이라 할 때, B[N]에 N개의 구슬이 들어 있는 칸을 찾는다. 그런 칸이 여러 개라면 아무 것이나 선택해도 상관없다. 만일 B[N]=N인 칸이 없다면 그 판은 패배이다.

위의 예제에서는 맨 첫 줄을 보면 된다. 3번 칸을 선택한 상황이다.

이제 고른 칸의 구슬을 Roumba와 B[1], B[2], ... , B[N-1]에 하나씩 고르게 나누어준다.

위의 시행을 계속 반복하여 모든 구슬이 Roumba로 들어간다면 게임을 성공적으로 마치게 되는 것이고, 이처럼 성공이 가능한 모든 게임판을 승리하는 게임판이라고 한다. 모든 정수 N에 대해, 구슬이 총 N개일 때의 승리하는 게임판은 항상 유일하다. 따라서 위에서의 Roumba를 뺀 보드판의 초기 상태 { 0, 1, 3 } 은 구슬이 4개일 때의 유일한 승리하는 게임판이다.

총 구슬의 개수 N이 주어지면 승리하는 게임판을 출력하라.

입력

첫 줄에 테스트 케이스의 수 P가 주어진다. (1 ≤ P ≤ 1000)

각 테스트 케이스는 테스트 케이스의 번호 T와 보드판에 들어갈 구슬의 총 개수 N으로 이루어져 있다.

출력

각 테스트 케이스마다 첫 줄에 테스트 케이스의 번호 T와 구슬이 하나 이상 담겨 있는 보드판의 마지막 위치 B를 출력한다.

그 후 승리하는 게임판의 상태를 B개의 정수로 출력하는데, 수는 10개 단위로 끊어서 출력해야 한다.

모든 테스트 케이스에서 B는 80을 넘지 않는다.

예제 입력 1

3
1 4
2 57
3 500

예제 출력 1

1 3
0 1 3
2 12
1 2 2 2 2 6 2 4 6 8
10 12
3 39
0 2 2 1 3 2 2 2 6 7
5 0 6 12 2 6 10 14 18 1
3 5 7 9 11 13 15 17 19 21
23 25 27 29 31 33 35 37 39
[{"problem_id":"10435","problem_lang":"0","title":"\ub9cc\uce7c\ub77c","description":"<p>\ub9cc\uce7c\ub77c\ub294 \ubcf4\ub4dc \uac8c\uc784\uc758 \ud55c \uc885\ub958\ub85c, \uc5ec\ub7ec \ubcc0\ud615 \ud310\uc774 \uc874\uc7ac\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \uc911 \uac00\uc7a5 \uac04\ub2e8\ud55c \uc885\ub958\uc778 1\uc778\uc6a9 \ub9cc\uce7c\ub77c \uac8c\uc784 Tchoukaillon\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcfc \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>Tchoukaillon\ub294 \uc5ec\ub7ec \uac1c\uc758 \ube48\uce78\uacfc \ud558\ub098\uc758 Roumba\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ubcf4\ub4dc \uc704\uc5d0\uc11c \uc9c4\ud589\ub41c\ub2e4.<\/p>\r\n\r\n<p><img src=\"https:\/\/www.acmicpc.net\/upload\/images2\/mancala.png\" \/><\/p>\r\n\r\n<p>\uac00\uc7a5 \uc67c\ucabd\uc758 \ube48\uce78\uc740 Roumba\uc774\uba70, \ucc98\uc74c\uc5d4 \ud56d\uc0c1 \ube44\uc5b4\uc788\ub294 \uc0c1\ud0dc\uc5ec\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc9c4\ud589\ub41c\ub2e4. \uc6b0\uc120, \uac01 \uce78\uc744 B[N]\uc774\ub77c \ud560 \ub54c, B[N]\uc5d0 N\uac1c\uc758 \uad6c\uc2ac\uc774 \ub4e4\uc5b4 \uc788\ub294 \uce78\uc744 \ucc3e\ub294\ub2e4. \uadf8\ub7f0 \uce78\uc774 \uc5ec\ub7ec \uac1c\ub77c\uba74 \uc544\ubb34 \uac83\uc774\ub098 \uc120\ud0dd\ud574\ub3c4 \uc0c1\uad00\uc5c6\ub2e4. \ub9cc\uc77c B[N]=N\uc778 \uce78\uc774 \uc5c6\ub2e4\uba74 \uadf8 \ud310\uc740 \ud328\ubc30\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc704\uc758 \uc608\uc81c\uc5d0\uc11c\ub294 \ub9e8 \uccab \uc904\uc744 \ubcf4\uba74 \ub41c\ub2e4. 3\ubc88 \uce78\uc744 \uc120\ud0dd\ud55c \uc0c1\ud669\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc81c \uace0\ub978 \uce78\uc758 \uad6c\uc2ac\uc744 Roumba\uc640 B[1], B[2], ... , B[N-1]\uc5d0 \ud558\ub098\uc529 \uace0\ub974\uac8c \ub098\ub204\uc5b4\uc900\ub2e4.<\/p>\r\n\r\n<p>\uc704\uc758 \uc2dc\ud589\uc744 \uacc4\uc18d \ubc18\ubcf5\ud558\uc5ec \ubaa8\ub4e0 \uad6c\uc2ac\uc774 Roumba\ub85c \ub4e4\uc5b4\uac04\ub2e4\uba74 \uac8c\uc784\uc744 \uc131\uacf5\uc801\uc73c\ub85c \ub9c8\uce58\uac8c \ub418\ub294 \uac83\uc774\uace0, \uc774\ucc98\ub7fc \uc131\uacf5\uc774 \uac00\ub2a5\ud55c \ubaa8\ub4e0 \uac8c\uc784\ud310\uc744 \uc2b9\ub9ac\ud558\ub294 \uac8c\uc784\ud310\uc774\ub77c\uace0 \ud55c\ub2e4. \ubaa8\ub4e0 \uc815\uc218 N\uc5d0 \ub300\ud574, \uad6c\uc2ac\uc774 \ucd1d N\uac1c\uc77c \ub54c\uc758 \uc2b9\ub9ac\ud558\ub294 \uac8c\uc784\ud310\uc740 \ud56d\uc0c1 \uc720\uc77c\ud558\ub2e4. \ub530\ub77c\uc11c \uc704\uc5d0\uc11c\uc758 Roumba\ub97c \ube80 \ubcf4\ub4dc\ud310\uc758 \ucd08\uae30 \uc0c1\ud0dc { 0, 1, 3 } \uc740 \uad6c\uc2ac\uc774 4\uac1c\uc77c \ub54c\uc758 \uc720\uc77c\ud55c \uc2b9\ub9ac\ud558\ub294 \uac8c\uc784\ud310\uc774\ub2e4.<\/p>\r\n\r\n<p>\ucd1d \uad6c\uc2ac\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c0\uba74 \uc2b9\ub9ac\ud558\ub294 \uac8c\uc784\ud310\uc744 \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 P\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; P &le; 1000)<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ubc88\ud638 T\uc640 \ubcf4\ub4dc\ud310\uc5d0 \ub4e4\uc5b4\uac08 \uad6c\uc2ac\uc758 \ucd1d \uac1c\uc218 N\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ubc88\ud638 T\uc640 \uad6c\uc2ac\uc774 \ud558\ub098 \uc774\uc0c1 \ub2f4\uaca8 \uc788\ub294 \ubcf4\ub4dc\ud310\uc758 \ub9c8\uc9c0\ub9c9 \uc704\uce58 B\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \ud6c4 \uc2b9\ub9ac\ud558\ub294 \uac8c\uc784\ud310\uc758 \uc0c1\ud0dc\ub97c B\uac1c\uc758 \uc815\uc218\ub85c \ucd9c\ub825\ud558\ub294\ub370, \uc218\ub294 10\uac1c \ub2e8\uc704\ub85c \ub04a\uc5b4\uc11c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c B\ub294 80\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10435","problem_lang":"1","title":"Mancala","description":"<p>Mancala is a family of board games played around the world, sometimes called sowing games, or count-and-capture games, which describes the game play. One simple variant is a solitaire game called Tchoukaillon which was described by V&eacute;ronique Gautheron. Tchoukaillon is played on a board respectively and an extra empty bin called Roumba on the left.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images2\/mancala.png\" style=\"height:376px; width:485px\" \/><\/p>\r\n\r\n<p>A single play consists on choosing a bin, n, for which b[n] = n (indicated by the darker circles in the diagram) and distributing the counters one per bin to the bins to the left including the Roumba (getting the next diagram below in the figure above). If there is no bin where b[n] = n, then the board is a losing board.<\/p>\r\n\r\n<p>If there is a sequence of plays which takes the initial board distribution to one in which every counter is in the Roumba, the initial distribution is called a winnable board. In the example above, 0, 1, 3, ... is a winnable board (the &quot;...&quot; indicates all the bins to the right of bin 3 contain 0). For each total number of counters, there is a unique distribution of the counters to bins to make a winnable board for that total count (so 0, 1, 3, ... is the only winnable board with 4 counters).<\/p>\r\n\r\n<p>Write a program which finds the winnable board for a total count input.<\/p>\r\n","input":"<p>The first line of input contains a single integer P, (1 &le; P &le; 1000), which is the number of data sets that follow. Each data set should be processed identically and independently.<\/p>\r\n\r\n<p>Each data set consists of a single line of input. It contains the data set number, K, followed by a single space, followed by the total count N (1 &le; N &le; 2000) of the winnable board to be found.<\/p>\r\n","output":"<p>For each data set there will be multiple lines of output. The first line of output contains the data set number, K, followed by a single space, followed by the index of the last bin, B, with a non-zero count. Input will be chosen so that B will be no more than 80. The first line of output for each dataset is followed by the bin counts b[1], b[2], ..., b[B], 10 per line separated by single spaces.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

채점

  • 제출한 후 다른 소스를 제출하려면 3초가 지나야 한다.