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문제

글은 단어로 이루어져 있고, 단어는 글자로 이루어져 있다. 현수는 단어를 총 W열의 원고지에 써넣으려고 한다. (원고지의 행의 개수는 무한하다) 현수의 좌우명은 "보기 좋은 떡이 먹기도 좋다"이다. 따라서, 원고지에 글을 쓸 때, 항상 아래와 같은 규칙을 지킨다.

1. 글에 포함되어 있는 단어의 순서를 뒤섞으면 안 된다. 아래 그림 중 왼쪽 그림은 "This is a pen"을 11열 원고지에 작성할 때 올바른 예이고, 오른쪽 그림은 올바르지 않은 예이다. (단어의 순서를 섞었다)

2. 같은 줄에 있는 두 단어 사이에는 공백이 적어도 한 칸 있어야 한다. 아래 그림은 단어와 단어 사이에 공백을 넣지 않았기 때문에, 올바르지 않은 예이다.

3. 단어는 그 글자수만큼 연속된 칸을 차지해야 한다. 한 단어를 두 줄에 나누어서 쓸 수 없고, 단어 내에 공백이 들어 있으면 안 된다. 아래 예는 단어에 포함되어 있는 글자가 연속되지 않아서 현수의 규칙을 지키지 않는 예이다.

4. 글은 양 변에 대해서 균등 정렬이 되어야 한다. 즉, 각 줄의 첫 번째 단어는 첫 번째 열에서 시작해어야 하고, 마지막 줄을 제외한 모든 줄의 마지막 단어는 마지막 열에서 끝나야 한다. 아래 그림은 양 변에 대해서 균등하지 않은 예이다.

글은 불필요한 긴 공백이 없을 때 아름다운 레이아웃이라고 한다. 즉, 제일 긴 연속된 공백의 길이가 최소가 되어야 한다. 예를 들어, 아래 그림은 "This is a pen"을 11열 원고지에 쓸 때, 현수의 규칙을 지키면서 가장 아름다운 레이아웃이다. 제일 긴 연속된 공백의 길이가 2이다. 또, 1번 조건의 아래 왼쪽 그림은 3이다.

글과 원고지의 열의 개수가 주어진다. 이때, 현수의 규칙을 지키면서 이 글을 원고지에 쓸 때, 가장 아름다운 레이아웃의 제일 긴 연속된 공백의 길이를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 W와 N이 주어진다. W는 원고지의 열의 개수이고, N은 글에 포함되어 있는 단어의 개수이다. (3 ≤ W ≤ 80,000, 2 ≤ N ≤ 50,000)

둘째 줄에는 단어의 길이 xi가 주어진다. xi는 i번째 단어의 길이이다. (1 ≤ xi ≤ (W-1)/2)

항상 문제의 조건을 만족하는 레이아웃이 존재한다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해서, 가장 아름다운 레이아웃의 제일 긴 연속된 공백의 길이를 출력한다.

예제 입력 1

11 4
4 2 1 3
5 7
1 1 1 2 2 1 2
11 7
3 1 3 1 3 3 4
100 3
30 30 39
30 3
2 5 3
0 0

예제 출력 1

2
1
2
40
1
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(\uc6d0\uace0\uc9c0\uc758 \ud589\uc758 \uac1c\uc218\ub294 \ubb34\ud55c\ud558\ub2e4) \ud604\uc218\uc758 \uc88c\uc6b0\uba85\uc740 &quot;\ubcf4\uae30 \uc88b\uc740 \ub5a1\uc774 \uba39\uae30\ub3c4 \uc88b\ub2e4&quot;\uc774\ub2e4. \ub530\ub77c\uc11c, \uc6d0\uace0\uc9c0\uc5d0 \uae00\uc744 \uc4f8 \ub54c, \ud56d\uc0c1 \uc544\ub798\uc640 \uac19\uc740 \uaddc\uce59\uc744 \uc9c0\ud0a8\ub2e4.<\/p>\r\n\r\n<p>1. \uae00\uc5d0 \ud3ec\ud568\ub418\uc5b4 \uc788\ub294 \ub2e8\uc5b4\uc758 \uc21c\uc11c\ub97c \ub4a4\uc11e\uc73c\uba74 \uc548 \ub41c\ub2e4. \uc544\ub798 \uadf8\ub9bc \uc911 \uc67c\ucabd \uadf8\ub9bc\uc740 &quot;This is a pen&quot;\uc744 11\uc5f4 \uc6d0\uace0\uc9c0\uc5d0 \uc791\uc131\ud560 \ub54c \uc62c\ubc14\ub978 \uc608\uc774\uace0, \uc624\ub978\ucabd \uadf8\ub9bc\uc740 \uc62c\ubc14\ub974\uc9c0 \uc54a\uc740 \uc608\uc774\ub2e4. (\ub2e8\uc5b4\uc758 \uc21c\uc11c\ub97c \uc11e\uc5c8\ub2e4)<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bs1(1).png\" style=\"height:70px; width:574px\" \/><\/p>\r\n\r\n<p>2. \uac19\uc740 \uc904\uc5d0 \uc788\ub294 \ub450 \ub2e8\uc5b4 \uc0ac\uc774\uc5d0\ub294 \uacf5\ubc31\uc774 \uc801\uc5b4\ub3c4 \ud55c \uce78 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \ub2e8\uc5b4\uc640 \ub2e8\uc5b4 \uc0ac\uc774\uc5d0 \uacf5\ubc31\uc744 \ub123\uc9c0 \uc54a\uc558\uae30 \ub54c\ubb38\uc5d0, \uc62c\ubc14\ub974\uc9c0 \uc54a\uc740 \uc608\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bs2(1).png\" style=\"height:68px; width:292px\" \/><\/p>\r\n\r\n<p>3. \ub2e8\uc5b4\ub294 \uadf8 \uae00\uc790\uc218\ub9cc\ud07c \uc5f0\uc18d\ub41c \uce78\uc744 \ucc28\uc9c0\ud574\uc57c \ud55c\ub2e4. \ud55c \ub2e8\uc5b4\ub97c \ub450 \uc904\uc5d0 \ub098\ub204\uc5b4\uc11c \uc4f8 \uc218 \uc5c6\uace0, \ub2e8\uc5b4 \ub0b4\uc5d0 \uacf5\ubc31\uc774 \ub4e4\uc5b4 \uc788\uc73c\uba74 \uc548 \ub41c\ub2e4. \uc544\ub798 \uc608\ub294 \ub2e8\uc5b4\uc5d0 \ud3ec\ud568\ub418\uc5b4 \uc788\ub294 \uae00\uc790\uac00 \uc5f0\uc18d\ub418\uc9c0 \uc54a\uc544\uc11c \ud604\uc218\uc758 \uaddc\uce59\uc744 \uc9c0\ud0a4\uc9c0 \uc54a\ub294 \uc608\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bs3.png\" style=\"height:75px; width:574px\" \/><\/p>\r\n\r\n<p>4. \uae00\uc740 \uc591 \ubcc0\uc5d0 \ub300\ud574\uc11c \uade0\ub4f1 \uc815\ub82c\uc774 \ub418\uc5b4\uc57c \ud55c\ub2e4. \uc989, \uac01 \uc904\uc758 \uccab \ubc88\uc9f8 \ub2e8\uc5b4\ub294 \uccab \ubc88\uc9f8 \uc5f4\uc5d0\uc11c \uc2dc\uc791\ud574\uc5b4\uc57c \ud558\uace0, \ub9c8\uc9c0\ub9c9 \uc904\uc744 \uc81c\uc678\ud55c \ubaa8\ub4e0 \uc904\uc758 \ub9c8\uc9c0\ub9c9 \ub2e8\uc5b4\ub294 \ub9c8\uc9c0\ub9c9 \uc5f4\uc5d0\uc11c \ub05d\ub098\uc57c \ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 \uc591 \ubcc0\uc5d0 \ub300\ud574\uc11c \uade0\ub4f1\ud558\uc9c0 \uc54a\uc740 \uc608\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bs4.png\" style=\"height:79px; width:584px\" \/><\/p>\r\n\r\n<p>\uae00\uc740 \ubd88\ud544\uc694\ud55c \uae34 \uacf5\ubc31\uc774 \uc5c6\uc744 \ub54c \uc544\ub984\ub2e4\uc6b4 \ub808\uc774\uc544\uc6c3\uc774\ub77c\uace0 \ud55c\ub2e4. \uc989, \uc81c\uc77c \uae34 \uc5f0\uc18d\ub41c \uacf5\ubc31\uc758 \uae38\uc774\uac00 \ucd5c\uc18c\uac00 \ub418\uc5b4\uc57c \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc544\ub798 \uadf8\ub9bc\uc740 &quot;This is a pen&quot;\uc744 11\uc5f4 \uc6d0\uace0\uc9c0\uc5d0 \uc4f8 \ub54c, \ud604\uc218\uc758 \uaddc\uce59\uc744 \uc9c0\ud0a4\uba74\uc11c \uac00\uc7a5 \uc544\ub984\ub2e4\uc6b4 \ub808\uc774\uc544\uc6c3\uc774\ub2e4. \uc81c\uc77c \uae34 \uc5f0\uc18d\ub41c \uacf5\ubc31\uc758 \uae38\uc774\uac00 2\uc774\ub2e4. \ub610, 1\ubc88 \uc870\uac74\uc758 \uc544\ub798 \uc67c\ucabd \uadf8\ub9bc\uc740 3\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/bs5.png\" style=\"height:71px; width:288px\" \/><\/p>\r\n\r\n<p>\uae00\uacfc \uc6d0\uace0\uc9c0\uc758 \uc5f4\uc758 \uac1c\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub54c, \ud604\uc218\uc758 \uaddc\uce59\uc744 \uc9c0\ud0a4\uba74\uc11c \uc774 \uae00\uc744 \uc6d0\uace0\uc9c0\uc5d0 \uc4f8 \ub54c, \uac00\uc7a5 \uc544\ub984\ub2e4\uc6b4 \ub808\uc774\uc544\uc6c3\uc758 \uc81c\uc77c \uae34 \uc5f0\uc18d\ub41c \uacf5\ubc31\uc758 \uae38\uc774\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 W\uc640 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. W\ub294 \uc6d0\uace0\uc9c0\uc758 \uc5f4\uc758 \uac1c\uc218\uc774\uace0, N\uc740 \uae00\uc5d0 \ud3ec\ud568\ub418\uc5b4 \uc788\ub294 \ub2e8\uc5b4\uc758 \uac1c\uc218\uc774\ub2e4. (3 &le; W &le; 80,000, 2 &le; N &le; 50,000)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \ub2e8\uc5b4\uc758 \uae38\uc774 x<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. xi\ub294 i\ubc88\uc9f8 \ub2e8\uc5b4\uc758 \uae38\uc774\uc774\ub2e4. (1 &le; x<sub>i<\/sub> &le; (W-1)\/2)<\/p>\r\n\r\n<p>\ud56d\uc0c1 \ubb38\uc81c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ub808\uc774\uc544\uc6c3\uc774 \uc874\uc7ac\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uac00\uc7a5 \uc544\ub984\ub2e4\uc6b4 \ub808\uc774\uc544\uc6c3\uc758 \uc81c\uc77c \uae34 \uc5f0\uc18d\ub41c \uacf5\ubc31\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3833","problem_lang":"1","title":"Beautiful Spacing","description":"<p>Text is a sequence of words, and a word consists of characters. Your task is to put words into a grid with W columns and su\ufb03ciently many lines. For the beauty of the layout, the following conditions have to be satis fied.<\/p>\r\n\r\n<p>1. The words in the text must be placed keeping their original order. The following figures show correct and incorrect layout examples for a 4 word text &quot;This is a pen&quot; into 11 columns.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lo1.png\" style=\"height:103px; width:583px\" \/><\/p>\r\n\r\n<p>2. Between two words adjacent in the same line, you must place at least one space character. You sometimes have to put more than one space in order to meet other conditions.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lo2.png\" style=\"height:107px; width:410px\" \/><\/p>\r\n\r\n<p>3. A word must occupy the same number of consecutive columns as the number of characters in it. You cannot break a single word into two or more by breaking it into lines or by inserting spaces.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lo3.png\" style=\"height:96px; width:575px\" \/><\/p>\r\n\r\n<p>4. The text must be justi ed to the both sides. That is, the fi rst word of a line must start from the fi rst column of the line, and except the last line, the last word of a line must end at the last column.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lo4.png\" style=\"height:110px; width:590px\" \/><\/p>\r\n\r\n<p>The text is the most beautifully laid out when there is no unnecessarily long spaces. For instance, the layout in Figure I.6 has at most 2 contiguous spaces, which is more beautiful than that in Figure I.1, having 3 contiguous spaces. Given an input text and the number of columns, please fi nd a layout such that the length of the longest contiguous spaces between words is minimum.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lo5.png\" style=\"height:107px; width:362px\" \/><\/p>\r\n","input":"<p>The input consists of multiple datasets, each in the following format.<\/p>\r\n\r\n<p>W, N, and xi are all integers. W is the number of columns (3 &le; W &le; 80, 000). N is the number of words (2 &le; N &le; 50, 000). xi is the number of characters in the i-th word (1 &le; xi &le; (W - 1)\/2). Note that the upper bound on xi assures that there always exists a layout satisfying the conditions<\/p>\r\n\r\n<p>The last dataset is followed by a line containing two zeros.<\/p>\r\n","output":"<p>For each dataset, print the smallest possible number of the longest contiguous spaces between words.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Japan > Asia Regional Contest 2012 in Tokyo I번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: tae