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문제

CSHS(Computer Science High School)의 실습실에는 총 M대의 컴퓨터가 일렬로 놓여있다. 이 컴퓨터는 왼쪽에 있는 것부터 순서대로 1~M의 번호가 매겨져 있다.

현재, 이 실습실에는 총 N명의 학생들이 이미 앉아있으며, 각각 A1, A2, ..., AN번 컴퓨터 앞에 앉아있다. 곧 있으면 자습시간이 시작되기 때문에 총 M-N명의 학생이 더 와서 컴퓨터를 사용할 것이다.

각 학생들은 다른 학생이 자기 컴퓨터의 모니터를 보는 것을 싫어하므로 다음과 같은 방법으로 자리를 잡을 것이다.

  • 우선 학생이 없는 연속한 컴퓨터들의 그룹 중 가장 컴퓨터가 많은 그룹을 선택한다. 만약 이런 그룹이 여러개라면 가장 왼쪽에 있는 그룹을 선택한다.
  • 그 다음, 선택한 그룹의 컴퓨터들 중 정 중앙에 있는 컴퓨터를 선택하여 자리를 잡는다. 만약 학생이 선택한 그룹의 컴퓨터가 짝수개인 경우 정중앙 2개의 컴퓨터 중 왼쪽에 있는 컴퓨터에 자리를 잡는다.

진환이는 Q명의 친구들과 함께 팀 프로젝트를 해야 하기 때문에 Q명의 친구들이 어디에 앉을 지 알아야 한다. 다행히 진환이는 각 친구가 몇 번째로 실습실에 들어갔는지 알고 있다. 진환이를 도와 각 친구들의 위치를 구하.

입력

첫 번째 줄에는 컴퓨터의 수 M, 이미 자리를 잡은 학생의 수 N, 친구의 수 Q가 주어진다.

두 번째 줄에는 N개의 정수가 주어지는데, 이 값은 자리를 잡은 학생의 위치 Ai를 나타낸다. 이미 자리를 잡은 학생들은 앞서 말한 방법으로 자리를 잡지 않았을 수도 있음에 유의하여라.

세 번째 줄에는 Q개의 정수가 주어지는데, 이 값은 각 친구가 실습실에 들어간 순서 Bi를 의미한다.

A와 B는 오름차순이다. 즉, 항상 1 ≤ A1 < A2 < . . . < AN ≤ M 와 1 ≤ B1 < B2 < . . . < BQ ≤ M를 만족한다.

출력

출력은 총 Q개의 줄로 이루어진다. i번째 줄에는 i번째 친구가 자리잡은 컴퓨터의 번호를 출력한다. 처리하는 정수의 범위가 32비트 정수를 넘어가므로 64비트 정수형 변수를 사용하도록 한다.

제한

모든 서브태스크에서 1 ≤ Q ≤ 105, N ≤ M 그리고 1 ≤ N ≤ 105를 만족한다.

서브태스크

번호배점제한
119

1 ≤ M ≤ 300 000

222

1 ≤ M ≤ 1014, BQ ≤ 300 000

359

1 ≤ M ≤ 1014

예제 입력 1

7 1 4
4
2 3 4 5

예제 출력 1

2
6
1
3

예제 입력 2

10 2 4
2 8
1 3 5 8

예제 출력 2

2
5
6
4

힌트

예제 2 설명

처음에는 2번 컴퓨터와 8번 컴퓨터에 학생이 있다.

추가적으로 오는 8명의 학생들은 순서대로 5, 3, 6, 9, 1, 4, 7, 10번 컴퓨터에 앉을 것이다.

[{"problem_id":"10755","problem_lang":"0","title":"\ucef4\ud4e8\ud130\uc2e4","description":"<p>CSHS(Computer Science High School)\uc758 \uc2e4\uc2b5\uc2e4\uc5d0\ub294 \ucd1d M\ub300\uc758 \ucef4\ud4e8\ud130\uac00 \uc77c\ub82c\ub85c \ub193\uc5ec\uc788\ub2e4. \uc774 \ucef4\ud4e8\ud130\ub294 \uc67c\ucabd\uc5d0 \uc788\ub294 \uac83\ubd80\ud130 \uc21c\uc11c\ub300\ub85c 1~M\uc758 \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud604\uc7ac, \uc774 \uc2e4\uc2b5\uc2e4\uc5d0\ub294 \ucd1d N\uba85\uc758 \ud559\uc0dd\ub4e4\uc774 \uc774\ubbf8 \uc549\uc544\uc788\uc73c\uba70, \uac01\uac01 A<sub>1<\/sub>, A<sub>2<\/sub>, ..., A<sub>N<\/sub>\ubc88 \ucef4\ud4e8\ud130 \uc55e\uc5d0 \uc549\uc544\uc788\ub2e4. \uace7 \uc788\uc73c\uba74 \uc790\uc2b5\uc2dc\uac04\uc774 \uc2dc\uc791\ub418\uae30 \ub54c\ubb38\uc5d0 \ucd1d M-N\uba85\uc758 \ud559\uc0dd\uc774 \ub354 \uc640\uc11c \ucef4\ud4e8\ud130\ub97c \uc0ac\uc6a9\ud560 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud559\uc0dd\ub4e4\uc740 \ub2e4\ub978 \ud559\uc0dd\uc774 \uc790\uae30 \ucef4\ud4e8\ud130\uc758 \ubaa8\ub2c8\ud130\ub97c \ubcf4\ub294 \uac83\uc744 \uc2eb\uc5b4\ud558\ubbc0\ub85c \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc790\ub9ac\ub97c \uc7a1\uc744 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc6b0\uc120 \ud559\uc0dd\uc774 \uc5c6\ub294 \uc5f0\uc18d\ud55c \ucef4\ud4e8\ud130\ub4e4\uc758 \uadf8\ub8f9 \uc911 \uac00\uc7a5 \ucef4\ud4e8\ud130\uac00 \ub9ce\uc740 \uadf8\ub8f9\uc744 \uc120\ud0dd\ud55c\ub2e4. \ub9cc\uc57d \uc774\ub7f0 \uadf8\ub8f9\uc774 \uc5ec\ub7ec\uac1c\ub77c\uba74 \uac00\uc7a5 \uc67c\ucabd\uc5d0 \uc788\ub294 \uadf8\ub8f9\uc744 \uc120\ud0dd\ud55c\ub2e4.<\/li>\r\n\t<li>\uadf8 \ub2e4\uc74c, \uc120\ud0dd\ud55c \uadf8\ub8f9\uc758 \ucef4\ud4e8\ud130\ub4e4 \uc911 \uc815 \uc911\uc559\uc5d0 \uc788\ub294 \ucef4\ud4e8\ud130\ub97c \uc120\ud0dd\ud558\uc5ec \uc790\ub9ac\ub97c \uc7a1\ub294\ub2e4. \ub9cc\uc57d \ud559\uc0dd\uc774 \uc120\ud0dd\ud55c \uadf8\ub8f9\uc758 \ucef4\ud4e8\ud130\uac00 \uc9dd\uc218\uac1c\uc778 \uacbd\uc6b0 \uc815\uc911\uc559 2\uac1c\uc758 \ucef4\ud4e8\ud130 \uc911 \uc67c\ucabd\uc5d0 \uc788\ub294 \ucef4\ud4e8\ud130\uc5d0 \uc790\ub9ac\ub97c \uc7a1\ub294\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc9c4\ud658\uc774\ub294 Q\uba85\uc758 \uce5c\uad6c\ub4e4\uacfc \ud568\uaed8 \ud300 \ud504\ub85c\uc81d\ud2b8\ub97c \ud574\uc57c \ud558\uae30 \ub54c\ubb38\uc5d0 Q\uba85\uc758 \uce5c\uad6c\ub4e4\uc774 \uc5b4\ub514\uc5d0 \uc549\uc744 \uc9c0 \uc54c\uc544\uc57c \ud55c\ub2e4. \ub2e4\ud589\ud788 \uc9c4\ud658\uc774\ub294 \uac01 \uce5c\uad6c\uac00 \uba87 \ubc88\uc9f8\ub85c \uc2e4\uc2b5\uc2e4\uc5d0 \ub4e4\uc5b4\uac14\ub294\uc9c0 \uc54c\uace0 \uc788\ub2e4. \uc9c4\ud658\uc774\ub97c \ub3c4\uc640 \uac01 \uce5c\uad6c\ub4e4\uc758 \uc704\uce58\ub97c \uad6c\ud558.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ucef4\ud4e8\ud130\uc758 \uc218 M, \uc774\ubbf8 \uc790\ub9ac\ub97c \uc7a1\uc740 \ud559\uc0dd\uc758 \uc218 N, \uce5c\uad6c\uc758 \uc218 Q\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 N\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370, \uc774 \uac12\uc740 \uc790\ub9ac\ub97c \uc7a1\uc740 \ud559\uc0dd\uc758 \uc704\uce58 A<sub>i<\/sub>\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uc774\ubbf8 \uc790\ub9ac\ub97c \uc7a1\uc740 \ud559\uc0dd\ub4e4\uc740 \uc55e\uc11c \ub9d0\ud55c \ubc29\ubc95\uc73c\ub85c \uc790\ub9ac\ub97c \uc7a1\uc9c0 \uc54a\uc558\uc744 \uc218\ub3c4 \uc788\uc74c\uc5d0 \uc720\uc758\ud558\uc5ec\ub77c.<\/p>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \uc904\uc5d0\ub294 Q\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370, \uc774 \uac12\uc740 \uac01 \uce5c\uad6c\uac00 \uc2e4\uc2b5\uc2e4\uc5d0 \ub4e4\uc5b4\uac04 \uc21c\uc11c B<sub>i<\/sub>\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>A\uc640 B\ub294 \uc624\ub984\ucc28\uc21c\uc774\ub2e4. \uc989, \ud56d\uc0c1 1 &le; A<sub>1<\/sub> &lt; A<sub>2<\/sub> &lt; . . . &lt; A<sub>N<\/sub> &le; M \uc640 1 &le; B<sub>1<\/sub> &lt; B<sub>2<\/sub> &lt; . . . &lt; B<sub>Q<\/sub> &le; M\ub97c \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ucd1d Q\uac1c\uc758 \uc904\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4. i\ubc88\uc9f8 \uc904\uc5d0\ub294 i\ubc88\uc9f8 \uce5c\uad6c\uac00 \uc790\ub9ac\uc7a1\uc740 \ucef4\ud4e8\ud130\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud55c\ub2e4. \ucc98\ub9ac\ud558\ub294 \uc815\uc218\uc758 \ubc94\uc704\uac00 32\ube44\ud2b8 \uc815\uc218\ub97c \ub118\uc5b4\uac00\ubbc0\ub85c 64\ube44\ud2b8 \uc815\uc218\ud615 \ubcc0\uc218\ub97c \uc0ac\uc6a9\ud558\ub3c4\ub85d \ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c 2 \uc124\uba85<\/p>\r\n\r\n<p>\ucc98\uc74c\uc5d0\ub294 2\ubc88 \ucef4\ud4e8\ud130\uc640 8\ubc88 \ucef4\ud4e8\ud130\uc5d0 \ud559\uc0dd\uc774 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ucd94\uac00\uc801\uc73c\ub85c \uc624\ub294 8\uba85\uc758 \ud559\uc0dd\ub4e4\uc740 \uc21c\uc11c\ub300\ub85c 5, 3, 6, 9, 1, 4, 7, 10\ubc88 \ucef4\ud4e8\ud130\uc5d0 \uc549\uc744 \uac83\uc774\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean","limit":"<p>\ubaa8\ub4e0 \uc11c\ube0c\ud0dc\uc2a4\ud06c\uc5d0\uc11c 1 &le; Q &le; 10<sup>5<\/sup>, N &le; M \uadf8\ub9ac\uace0 1 &le; N &le; 10<sup>5<\/sup>\ub97c \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n","subtask1":"<p>1 &le; M &le;&nbsp;300 000<\/p>\r\n","subtask2":"<p>1 &le; M &le; 10<sup>14<\/sup>, B<sub>Q<\/sub> &le; 300 000<\/p>\r\n","subtask3":"<p>1 &le; M &le; 10<sup>14<\/sup><\/p>\r\n"},{"problem_id":"10755","problem_lang":"1","title":"OGLEDALA","description":"<p>There are M modern washbasins numbered from 1 to M from left to right in the ladies&rsquo; room of an enormous shopping centre.<\/p>\r\n\r\n<p>Currently, there are N ladies in the restroom (numbered from 1 to N) and they&rsquo;ve occupied the washbasins with numbers A<sub>1<\/sub>, A<sub>2<\/sub>, . . . , A<sub>N<\/sub> . Soon there will be M &minus; N more ladies arriving (numbered from N + 1 to M in the order of arrival) that will occupy all the remaining available washbasins. The ladies arriving primarily want their privacy, so each of them always chooses an available washbasin by the following procedure:<\/p>\r\n\r\n<ul>\r\n\t<li>First she finds the largest consecutive series of available washbasins. If there is more than one, she chooses the leftmost.<\/li>\r\n\t<li>After that, she occupies the middle washbasin in the chosen series. If the series is of even length, she chooses the left of the two middle washbasins.<\/li>\r\n<\/ul>\r\n\r\n<p>It is safe to assume that none of the ladies will leave the washbasin in the foreseeable future.<\/p>\r\n\r\n<p>Write a programme that will, for each of Q given integers B<sub>i<\/sub>, determine the label of the washbasin that will be occupied by the lady marked with B<sub>i<\/sub>.<\/p>\r\n","input":"<p>The first line of input contains integers M, N and Q &ndash; the number of washbasins, the initial number of ladies in the restroom and the number of ladies for which you need to determine which washbasin they will use.<\/p>\r\n\r\n<p>The second line of input contains N space-separated integers, the ith of those numbers is A<sub>i<\/sub> &ndash; the label of the washbasin that is being used by lady i.<\/p>\r\n\r\n<p>The third line of input contains Q space-separated integers, the ith of those numbers is B<sub>i<\/sub> &ndash; the label of the lady for which we want to know which washbasin she will use.<\/p>\r\n\r\n<p>The first N ladies in the restroom haven&rsquo;t necessarily chosen their washbasins using the procedure described in the task.<\/p>\r\n\r\n<p>The arrays A and B are strictly increasing. In other words, it holds 1 &le; A<sub>1<\/sub> &lt; A<sub>2<\/sub> &lt; . . . &lt; A<sub>N<\/sub> &le; M and 1 &le; B<sub>1<\/sub> &lt; B<sub>2<\/sub> &lt; . . . &lt; B<sub>Q<\/sub> &le; M.<\/p>\r\n","output":"<p>Output Q lines. The ith line must contain the label of the washbasin that will be used by the lady labeled B<sub>i<\/sub>.<\/p>\r\n\r\n<p>Please note: We recommend that you use a 64-bit integer data type (int64 in Pascal, long long in C\/C++).<\/p>\r\n","hint":"<p>Clarification of the second example: The first two ladies occupy the washbasins 2 and 8 (respectively). The remaining ladies occupy the washbasins 5, 3, 6, 9, 1, 4, 7 and 10, respectively.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","limit":"<p>In all subtasks, it will hold 1 &le; Q &le; 10<sup>5<\/sup>, N &le; M and 1 &le; N &le; 10<sup>5<\/sup>.<\/p>\r\n","subtask1":"<p>1 &le; M &le;&nbsp;300 000<\/p>\r\n","subtask2":"<p>1 &le; M &le; 10<sup>14<\/sup>, B<sub>Q<\/sub> &le; 300 000<\/p>\r\n","subtask3":"<p>1 &le; M &le; 10<sup>14<\/sup><\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.