시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 128 MB 45 29 24 63.158%

문제

남극의 한 빙하 지대 어딘가에 펭귄 여러 마리가 살고 있다. 각 펭귄들은 바다에 떠 있는 여러 얼음 조각 위에 나뉘어 서 있다. 한 얼음 조각 위에 여러 마리의 펭귄이 있을 수도 있으며, 펭귄이 없는 빈 얼음 조각도 있을 수 있다.

펭귄은 사회성이 높은 동물이기 때문에 한 개의 얼음 위에 모두 모이고 싶다. 펭귄들은 얼음 조각들 중 하나를 도착지로 정해서 얼음과 얼음 사이를 점프해 오가며 도착지 위로 모두 모일 것이다. 단, 펭귄은 날 수 없기 때문에 많이 먼 얼음으로는 점프해서 가지 못한다.

게다가 지구 온난화 때문에 얼음 조각들이 녹고 있어서 몇몇 얼음 조각들은 펭귄이 밟았을 때 부서져 바다 아래로 가라앉아 버릴 수도 있다. 펭귄들은 얼음에 대해서는 아주 전문가이기 때문에 정확히 몇 번 밟아야 얼음이 가라앉는지 알 수 있다.

펭귄이 점프하여 다른 얼음으로 도약할 때 펭귄이 딛고 있던 얼음은 손상된다. 하지만 펭귄이 어떤 얼음으로 착지할 때 그 얼음은 손상되지 않는다.

펭귄들이 어떤 얼음 위로 모여야 다 모일 수 있을까?

얼음 조각 5개와 펭귄 세 마리가 있는 예제

입력

첫 줄에 테스트 케이스의 수 T가 주어진다. ( T ≤ 100 )

각 테스트 케이스는 다음과 같이 구성되어 있다.

  • 첫 줄에 얼음 조각의 개수 N (1 ≤ N ≤ 100)과 펭귄들이 점프할 수 있는 최대 거리 D ( 0 ≤ D ≤ 100000 ). D는 실수 범위에서 주어진다.
  • N줄에 걸쳐 정수 xi, yi, ni, mi
    • xi, yi는 좌표로 나타낸 얼음의 위치 ( -10000 ≤ xi, yi ≤ 10000 )
    • ni 는 그 얼음 위에 서 있는 펭귄의 수 ( 0 ≤ ni ≤ 10 )
    • mi는 펭귄이 그 얼음을 밟고 도약할 수 있는 최대 횟수 ( 1 ≤ mi ≤ 200 )

출력

각 테스트 케이스마다 펭귄들이 모두 모일 수 있는 얼음 조각의 번호를 공백으로 구분하여 오름차순으로 출력한다.

얼음 조각의 번호는 0부터 시작하여 입력으로 주어진 순서대로이며, 만일 어떤 얼음으로도 펭귄들이 다 모일 수 없을 경우 -1을 출력한다.

예제 입력 1

2
5 3.5
1 1 1 1
2 3 0 1
3 5 1 1
5 1 1 1
5 4 0 1
3 1.1
-1 0 5 10
0 0 3 9
2 0 1 1

예제 출력 1

1 2 4
-1
[{"problem_id":"3692","problem_lang":"0","title":"\ud3ad\uadc4\ub4e4\uc758 \ud589\uc9c4","description":"<p>\ub0a8\uadf9\uc758 \ud55c \ube59\ud558 \uc9c0\ub300 \uc5b4\ub518\uac00\uc5d0 \ud3ad\uadc4 \uc5ec\ub7ec \ub9c8\ub9ac\uac00 \uc0b4\uace0 \uc788\ub2e4. \uac01 \ud3ad\uadc4\ub4e4\uc740 \ubc14\ub2e4\uc5d0 \ub5a0 \uc788\ub294 \uc5ec\ub7ec \uc5bc\uc74c \uc870\uac01 \uc704\uc5d0 \ub098\ub258\uc5b4 \uc11c \uc788\ub2e4. \ud55c \uc5bc\uc74c \uc870\uac01 \uc704\uc5d0 \uc5ec\ub7ec \ub9c8\ub9ac\uc758 \ud3ad\uadc4\uc774 \uc788\uc744 \uc218\ub3c4 \uc788\uc73c\uba70, \ud3ad\uadc4\uc774 \uc5c6\ub294 \ube48 \uc5bc\uc74c \uc870\uac01\ub3c4 \uc788\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud3ad\uadc4\uc740 \uc0ac\ud68c\uc131\uc774 \ub192\uc740 \ub3d9\ubb3c\uc774\uae30 \ub54c\ubb38\uc5d0 \ud55c \uac1c\uc758 \uc5bc\uc74c \uc704\uc5d0 \ubaa8\ub450 \ubaa8\uc774\uace0 \uc2f6\ub2e4. \ud3ad\uadc4\ub4e4\uc740 \uc5bc\uc74c \uc870\uac01\ub4e4 \uc911 \ud558\ub098\ub97c \ub3c4\ucc29\uc9c0\ub85c \uc815\ud574\uc11c \uc5bc\uc74c\uacfc \uc5bc\uc74c \uc0ac\uc774\ub97c \uc810\ud504\ud574 \uc624\uac00\uba70 \ub3c4\ucc29\uc9c0 \uc704\ub85c \ubaa8\ub450 \ubaa8\uc77c \uac83\uc774\ub2e4. \ub2e8, \ud3ad\uadc4\uc740 \ub0a0 \uc218 \uc5c6\uae30 \ub54c\ubb38\uc5d0 \ub9ce\uc774 \uba3c \uc5bc\uc74c\uc73c\ub85c\ub294 \uc810\ud504\ud574\uc11c \uac00\uc9c0 \ubabb\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac8c\ub2e4\uac00 \uc9c0\uad6c \uc628\ub09c\ud654 \ub54c\ubb38\uc5d0 \uc5bc\uc74c \uc870\uac01\ub4e4\uc774 \ub179\uace0 \uc788\uc5b4\uc11c \uba87\uba87 \uc5bc\uc74c \uc870\uac01\ub4e4\uc740 \ud3ad\uadc4\uc774 \ubc1f\uc558\uc744 \ub54c \ubd80\uc11c\uc838 \ubc14\ub2e4 \uc544\ub798\ub85c \uac00\ub77c\uc549\uc544 \ubc84\ub9b4 \uc218\ub3c4 \uc788\ub2e4. \ud3ad\uadc4\ub4e4\uc740 \uc5bc\uc74c\uc5d0 \ub300\ud574\uc11c\ub294 \uc544\uc8fc \uc804\ubb38\uac00\uc774\uae30 \ub54c\ubb38\uc5d0 \uc815\ud655\ud788 \uba87 \ubc88 \ubc1f\uc544\uc57c \uc5bc\uc74c\uc774 \uac00\ub77c\uc549\ub294\uc9c0 \uc54c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud3ad\uadc4\uc774 \uc810\ud504\ud558\uc5ec \ub2e4\ub978 \uc5bc\uc74c\uc73c\ub85c \ub3c4\uc57d\ud560 \ub54c \ud3ad\uadc4\uc774 \ub51b\uace0 \uc788\ub358 \uc5bc\uc74c\uc740 \uc190\uc0c1\ub41c\ub2e4. \ud558\uc9c0\ub9cc \ud3ad\uadc4\uc774 \uc5b4\ub5a4 \uc5bc\uc74c\uc73c\ub85c \ucc29\uc9c0\ud560 \ub54c \uadf8 \uc5bc\uc74c\uc740 \uc190\uc0c1\ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\ud3ad\uadc4\ub4e4\uc774 \uc5b4\ub5a4 \uc5bc\uc74c \uc704\ub85c \ubaa8\uc5ec\uc57c \ub2e4 \ubaa8\uc77c \uc218 \uc788\uc744\uae4c?<\/p>\r\n\r\n<p><img src=\"\/upload\/images2\/penguin.png\" style=\"height:297.529411764706px; width:281px\" \/><\/p>\r\n\r\n<p>\uc5bc\uc74c \uc870\uac01 5\uac1c\uc640 \ud3ad\uadc4 \uc138 \ub9c8\ub9ac\uac00 \uc788\ub294 \uc608\uc81c<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. ( T &le; 100 )<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\uc131\ub418\uc5b4 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab \uc904\uc5d0 \uc5bc\uc74c \uc870\uac01\uc758 \uac1c\uc218 N (1 &le; N &le; 100)\uacfc \ud3ad\uadc4\ub4e4\uc774 \uc810\ud504\ud560 \uc218 \uc788\ub294 \ucd5c\ub300 \uac70\ub9ac D ( 0 &le; D &le; 100000 ). D\ub294 \uc2e4\uc218 \ubc94\uc704\uc5d0\uc11c \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\r\n\t<li>N\uc904\uc5d0 \uac78\uccd0 \uc815\uc218 xi, yi, ni, mi\r\n\t<ul>\r\n\t\t<li>xi, yi\ub294 \uc88c\ud45c\ub85c \ub098\ud0c0\ub0b8 \uc5bc\uc74c\uc758 \uc704\uce58 ( -10000 &le; xi, yi &le; 10000 )<\/li>\r\n\t\t<li>ni \ub294 \uadf8 \uc5bc\uc74c \uc704\uc5d0 \uc11c \uc788\ub294 \ud3ad\uadc4\uc758 \uc218 ( 0 &le; ni &le; 10 )<\/li>\r\n\t\t<li>mi\ub294 \ud3ad\uadc4\uc774 \uadf8 \uc5bc\uc74c\uc744 \ubc1f\uace0 \ub3c4\uc57d\ud560 \uc218 \uc788\ub294 \ucd5c\ub300 \ud69f\uc218 ( 1 &le; mi &le; 200 )<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud3ad\uadc4\ub4e4\uc774 \ubaa8\ub450 \ubaa8\uc77c \uc218 \uc788\ub294 \uc5bc\uc74c \uc870\uac01\uc758 \ubc88\ud638\ub97c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc5bc\uc74c \uc870\uac01\uc758 \ubc88\ud638\ub294 0\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c\uc774\uba70, \ub9cc\uc77c \uc5b4\ub5a4 \uc5bc\uc74c\uc73c\ub85c\ub3c4 \ud3ad\uadc4\ub4e4\uc774 \ub2e4 \ubaa8\uc77c \uc218 \uc5c6\uc744 \uacbd\uc6b0 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3692","problem_lang":"1","title":"March of the Penguins","description":"<p>Somewhere near the south pole, a number of penguins are standing on a number of ice floes. Being social animals, the penguins would like to get together, all on the same floe. The penguins do not want to get wet, so they have use their limited jump distance to get together by jumping from piece to piece. However, temperatures have been high lately, and the floes are showing cracks, and they get damaged further by the force needed to jump to another floe. Fortunately the penguins are real experts on cracking ice floes, and know exactly how many times a penguin can jump off each floe before it disintegrates and disappears. Landing on an ice floe does not damage it. You have to help the penguins find all floes where they can meet.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images2\/penguin.png\" style=\"height:216px; width:204px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">A sample layout of ice floes with 3 penguins on them.<\/p>\r\n","input":"<p>On the first line one positive number: the number of testcases, at most 100. After that per testcase:<\/p>\r\n\r\n<ul>\r\n\t<li>One line with the integer N (1 &le; N &le; 100) and a floating-point number D (0 &le; D &le; 100 000), denoting the number of ice pieces and the maximum distance a penguin can jump.<\/li>\r\n\t<li>&nbsp;N lines, each line containing xi, yi, ni and mi, denoting for each ice piece its X and Y coordinate, the number of penguins on it and the maximum number of times a penguin can jump off this piece before it disappears (&minus;10 000 &le; xi, yi &le; 10 000, 0 &le; ni &le; 10, 1 &le; mi &le; 200).<\/li>\r\n<\/ul>\r\n","output":"<p>Per testcase:<\/p>\r\n\r\n<ul>\r\n\t<li>One line containing a space-separated list of 0-based indices of the pieces on which all penguins can meet. If no such piece exists, output a line with the single number -1.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]