시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

은기는 음이 아닌 정수 n개로 이루어진 수열을 이용해 시간을 떼우고 있다. 은기는 수열을 총 k+1개로 나누어야 하고, 각 부분은 비어있지 않아야 한다. 수열을 k+1개로 나누러면, 아래와 같은 과정을 k번 반복해야 한다.

  1. 원소를 두 개 이상 가지고 있는 부분을 고른다. (가장 처음에는 수열 전체밖에 없다)
  2. 임의의 두 원소 사이를 기준으로 수열을 두 부분으로 나눈다.

위의 과정을 할 때마다 얻게되는 점수는 새로 나누어진 각 부분에 들어있는 원소의 합을 곱한 것이다. 위의 과정을 k번 반복하면서 은기가 얻을 수 있는 점수의 최댓값을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 두 정수 n과 k가 주어진다. (2 ≤ n ≤ 100,000, 1 ≤ k ≤ min(n-1, 200)) 둘째 줄에는 수열을 나타내는 음이 아닌 정수 n개 a1, a2, ..., an이 주어진다. (0 ≤ ai ≤ 104)

출력

첫째 줄에 얻을 수 있는 가장 큰 점수를 출력한다. 둘째 줄에는 그러한 점수를 얻기 위해 몇 번째 원소 다음에 수열을 나누어야 하는지 순서대로 출력한다. 가능한 답이 여러개라면, 아무거나 출력한다.

예제 입력 1

7 3
4 1 3 4 0 2 3

예제 출력 1

108
1 3 5

힌트

아래와 같은 과정으로 수열을 나누면 108점을 얻을 수 있다.

  • 현재 수열은 (4, 1, 3, 4, 0, 2, 3)이다. 첫 번째 원소 다음에서 수열을 나누면 4 × (1 + 3 + 4 + 0 + 2 + 3) = 52점을 얻게 된다.
  • 현재 두 부분으로 나누어져 있다. (4), (1, 3, 4, 0, 2, 3) 3번째 원소 다음에서 수열을 나누면 (1 + 3) × (4 + 0 + 2 + 3) = 36점을 얻게 된다.
  • 이제 총 세 부분으로 나누어져 있다. (4), (1, 3), (4, 0, 2, 3) 5번째 원소 다음에서 수열을 나누면 (4 + 0) × (2 + 3) = 20점을 얻게 된다.

수열은 총 4개의 부분 (4), (1, 3), (4, 0), (2, 3) 으로 나누어지게 되고, 은기가 얻은 점수는 52 + 36 + 20 = 108점이다.

[{"problem_id":"10067","problem_lang":"0","title":"\uc218\uc5f4 \ub098\ub204\uae30","description":"<p>\uc740\uae30\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218 n\uac1c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc218\uc5f4\uc744 \uc774\uc6a9\ud574 \uc2dc\uac04\uc744 \ub5bc\uc6b0\uace0 \uc788\ub2e4. \uc740\uae30\ub294 \uc218\uc5f4\uc744 \ucd1d k+1\uac1c\ub85c \ub098\ub204\uc5b4\uc57c \ud558\uace0, \uac01 \ubd80\ubd84\uc740 \ube44\uc5b4\uc788\uc9c0 \uc54a\uc544\uc57c \ud55c\ub2e4. \uc218\uc5f4\uc744 k+1\uac1c\ub85c \ub098\ub204\ub7ec\uba74, \uc544\ub798\uc640 \uac19\uc740 \uacfc\uc815\uc744 k\ubc88 \ubc18\ubcf5\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uc6d0\uc18c\ub97c \ub450 \uac1c \uc774\uc0c1 \uac00\uc9c0\uace0 \uc788\ub294 \ubd80\ubd84\uc744 \uace0\ub978\ub2e4. (\uac00\uc7a5 \ucc98\uc74c\uc5d0\ub294 \uc218\uc5f4 \uc804\uccb4\ubc16\uc5d0 \uc5c6\ub2e4)<\/li>\r\n\t<li>\uc784\uc758\uc758 \ub450 \uc6d0\uc18c \uc0ac\uc774\ub97c \uae30\uc900\uc73c\ub85c \uc218\uc5f4\uc744 \ub450 \ubd80\ubd84\uc73c\ub85c \ub098\ub208\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc704\uc758 \uacfc\uc815\uc744 \ud560 \ub54c\ub9c8\ub2e4 \uc5bb\uac8c\ub418\ub294 \uc810\uc218\ub294 \uc0c8\ub85c \ub098\ub204\uc5b4\uc9c4 \uac01 \ubd80\ubd84\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uc6d0\uc18c\uc758 \ud569\uc744 \uacf1\ud55c \uac83\uc774\ub2e4. \uc704\uc758 \uacfc\uc815\uc744 k\ubc88 \ubc18\ubcf5\ud558\uba74\uc11c \uc740\uae30\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\uc758 \ucd5c\ub313\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 n\uacfc k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; n &le; 100,000, 1 &le; k &le; min(n-1, 200)) \ub458\uc9f8 \uc904\uc5d0\ub294 \uc218\uc5f4\uc744 \ub098\ud0c0\ub0b4\ub294 \uc74c\uc774 \uc544\ub2cc \uc815\uc218 n\uac1c a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>n<\/sub>\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; a<sub>i<\/sub> &le; 10<sup>4<\/sup>)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc5bb\uc744 \uc218 \uc788\ub294 \uac00\uc7a5 \ud070 \uc810\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uadf8\ub7ec\ud55c \uc810\uc218\ub97c \uc5bb\uae30 \uc704\ud574 \uba87 \ubc88\uc9f8 \uc6d0\uc18c \ub2e4\uc74c\uc5d0 \uc218\uc5f4\uc744 \ub098\ub204\uc5b4\uc57c \ud558\ub294\uc9c0 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud55c\ub2e4. \uac00\ub2a5\ud55c \ub2f5\uc774 \uc5ec\ub7ec\uac1c\ub77c\uba74, \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc544\ub798\uc640 \uac19\uc740 \uacfc\uc815\uc73c\ub85c \uc218\uc5f4\uc744 \ub098\ub204\uba74 108\uc810\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ud604\uc7ac \uc218\uc5f4\uc740 (4, 1, 3, 4, 0, 2, 3)\uc774\ub2e4. \uccab \ubc88\uc9f8 \uc6d0\uc18c \ub2e4\uc74c\uc5d0\uc11c \uc218\uc5f4\uc744 \ub098\ub204\uba74 4 &times; (1 + 3 + 4 + 0 + 2 + 3) = 52\uc810\uc744 \uc5bb\uac8c \ub41c\ub2e4.<\/li>\r\n\t<li>\ud604\uc7ac \ub450 \ubd80\ubd84\uc73c\ub85c \ub098\ub204\uc5b4\uc838 \uc788\ub2e4. (4), (1, 3, 4, 0, 2, 3) 3\ubc88\uc9f8 \uc6d0\uc18c \ub2e4\uc74c\uc5d0\uc11c \uc218\uc5f4\uc744 \ub098\ub204\uba74 (1 + 3) &times; (4 + 0 + 2 + 3) = 36\uc810\uc744 \uc5bb\uac8c \ub41c\ub2e4.<\/li>\r\n\t<li>\uc774\uc81c \ucd1d \uc138 \ubd80\ubd84\uc73c\ub85c \ub098\ub204\uc5b4\uc838 \uc788\ub2e4. (4), (1, 3), (4, 0, 2, 3) 5\ubc88\uc9f8 \uc6d0\uc18c \ub2e4\uc74c\uc5d0\uc11c \uc218\uc5f4\uc744 \ub098\ub204\uba74 (4 + 0) &times; (2 + 3) = 20\uc810\uc744 \uc5bb\uac8c \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc218\uc5f4\uc740 \ucd1d 4\uac1c\uc758 \ubd80\ubd84 (4), (1, 3), (4, 0), (2, 3) \uc73c\ub85c \ub098\ub204\uc5b4\uc9c0\uac8c \ub418\uace0, \uc740\uae30\uac00 \uc5bb\uc740 \uc810\uc218\ub294 52 + 36 + 20 = 108\uc810\uc774\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10067","problem_lang":"1","title":"Split the sequence","description":"<p>You are playing a game with a sequence of n non-negative integers. In this game you have to split the sequence into k + 1 non-empty parts. To obtain k + 1 parts you repeat the following steps k times:<\/p>\r\n\r\n<ol>\r\n\t<li>Choose any part with more than one element (initially you have only one part &ndash; the whole sequence).<\/li>\r\n\t<li>Split it between any two elements to get two new non-empty parts.<\/li>\r\n<\/ol>\r\n\r\n<p>Each time after these steps you gain the number of points which is equal to product of sums of elements of each new part. You want to maximize the total number of points you gain.<\/p>\r\n","input":"<p>The first line of the input file contains two integers n and k (2 &le; n &le; 100000, 1 &le; k &le; min(n &minus; 1, 200)). The second line of input contains n non-negative integers a<sub>1<\/sub>, a<sub>2<\/sub>, . . . , a<sub>n<\/sub> (0 &le; a<sub>i<\/sub> &le; 10<sup>4<\/sup>) &ndash; the sequence.<\/p>\r\n","output":"<p>On the first line output the largest total number of points you can gain. On the second line output k integers between 1 and n &minus; 1 &mdash; the positions of elements after which you have to split the sequence to gain the largest total number of points. If there are more than one way to gain the largest number of points output any one of them.<\/p>\r\n","hint":"<p>In the first sample you can gain 108 points by the following way:<\/p>\r\n\r\n<ul>\r\n\t<li>Initially you have the whole sequence (4, 1, 3, 4, 0, 2, 3) as one part. You will split the sequence after 1st element and gain 4 &times; (1 + 3 + 4 + 0 + 2 + 3) = 52 points.<\/li>\r\n\t<li>You have two parts (4), (1, 3, 4, 0, 2, 3). You will split the sequence after 3rd element and gain (1 + 3) &times; (4 + 0 + 2 + 3) = 36 points.<\/li>\r\n\t<li>You have three parts (4), (1,3), (4, 0, 2, 3). You will split the sequence after 5th element and gain (4 + 0) &times; (2 + 3) = 20 points.<\/li>\r\n<\/ul>\r\n\r\n<p>So, after the steps taken above you get four parts (4), (1,3), (4,0), (2, 3) and gain 52 + 36 + 20 = 108 points.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > Asia-Pacific Informatics Olympiad > APIO 2014 2번