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문제

요즘 이상한 뉴스가 너무 많아서 그런지, 재현이의 성격은 점점 반사회적이고 폭력적으로 변했다. 얼마 전, 재현 이는 결국 학교의 3D 프린터를 사용해서 모형 권총을 프린트하고, 혼자 이상한 게임을 하기 시작했다.

재현이는 많은 두더지굴이 있는 잔디밭에서 게임을 시작했다. 잔디밭에는 n개의 두더지굴이 있으며, 두더지굴은 1번부터 n번까지 순서대로 번호가 부여되어 있다. 원형으로 늘어져 있으니, 1번 굴과 2번 굴, 2번 굴과 3번 굴, ..., n번 굴과 1번 굴은 인접해 있다.

현재 각각의 굴에는 ai 마리의 두더지가 있고, 재현이는 모형 권총으로 이들을 쫓아낼 계획이다. 재현이가 모형 권총을 쏴서 i번 굴에 있는 두더지에게 겁을 주면, 그 굴에 있는 두더지들이 겁을 먹고 도망가게 된다. (모형이라 죽지는 않는다.) 뿐만 아니라, 그 굴과 인접한 양 옆 두개의 굴에 있는 두더지들도 겁을 먹어서, 인접한 굴로 이동하게 된다. 당연히, 인접한 굴이라 하면 i번 굴은 아니다.

예를 들어, 10번 굴에 겁을 줬다면, 10번 굴에 있는 두더지는 모두 굴을 탈출하고, 9번 굴에 있는 두더지는 8번 굴로 도망가고, 11번 굴에 있는 두더지는 12번 굴로 도망간다.

재현이는 3D 프린터로 k개의 총알을 만들었고, 최대한 많은 두더지를 쫓아내고 싶다. 총을 k번 이하로 사용했을 때, 최대 몇 마리의 두더지가 굴을 탈출하는가?

입력

첫번째 줄에 두더지굴의 수 n, 총의 최대 사용 가능 수 k가 주어진다. (5 ≤ n ≤ 2000, 1 ≤ k ≤ n)

이후 n개의 정수 a1, a2, ..., an가 주어진다. (0 ≤ ai ≤ 106) i번째 굴에 ai마리의 두더지가 산다는 것을 의미한다.

출력

총을 k번 이하로 사용했을 때, 탈출시킬 수 있는 두더지 수의 최댓값을 출력한다.

예제 입력 1

5 2
6 1 5 3 4

예제 출력 1

13

힌트

초기 두더지 굴의 상태는 [6, 1, 5, 3, 4] 이다.

첫번째로, 재현이는 1번째 굴에 총을 쏴서, 6마리의 두더지를 탈출시킨다. 두더지 굴의 상태는 [0, 0, 6, 7, 0]이 된다.

이제, 재현이는 4번째 굴에 총을 쏴서, 7마리의 두더지를 탈출시킨다. 총 13마리가 탈출한다.

[{"problem_id":"7984","problem_lang":"0","title":"\ub450\ub354\uc9c0 \uc7a1\uae30","description":"<p>\uc694\uc998 \uc774\uc0c1\ud55c \ub274\uc2a4\uac00 \ub108\ubb34 \ub9ce\uc544\uc11c \uadf8\ub7f0\uc9c0, \uc7ac\ud604\uc774\uc758 \uc131\uaca9\uc740 \uc810\uc810 \ubc18\uc0ac\ud68c\uc801\uc774\uace0 \ud3ed\ub825\uc801\uc73c\ub85c \ubcc0\ud588\ub2e4. \uc5bc\ub9c8 \uc804, \uc7ac\ud604 \uc774\ub294 \uacb0\uad6d \ud559\uad50\uc758 3D \ud504\ub9b0\ud130\ub97c \uc0ac\uc6a9\ud574\uc11c \ubaa8\ud615 \uad8c\ucd1d\uc744 \ud504\ub9b0\ud2b8\ud558\uace0, \ud63c\uc790 \uc774\uc0c1\ud55c \uac8c\uc784\uc744 \ud558\uae30 \uc2dc\uc791\ud588\ub2e4.<\/p>\r\n\r\n<p>\uc7ac\ud604\uc774\ub294 \ub9ce\uc740 \ub450\ub354\uc9c0\uad74\uc774 \uc788\ub294 \uc794\ub514\ubc2d\uc5d0\uc11c \uac8c\uc784\uc744 \uc2dc\uc791\ud588\ub2e4. \uc794\ub514\ubc2d\uc5d0\ub294 n\uac1c\uc758 \ub450\ub354\uc9c0\uad74\uc774 \uc788\uc73c\uba70, \ub450\ub354\uc9c0\uad74\uc740 1\ubc88\ubd80\ud130 n\ubc88\uae4c\uc9c0 \uc21c\uc11c\ub300\ub85c \ubc88\ud638\uac00 \ubd80\uc5ec\ub418\uc5b4 \uc788\ub2e4. \uc6d0\ud615\uc73c\ub85c \ub298\uc5b4\uc838 \uc788\uc73c\ub2c8, 1\ubc88 \uad74\uacfc 2\ubc88 \uad74, 2\ubc88 \uad74\uacfc 3\ubc88 \uad74, ..., n\ubc88 \uad74\uacfc 1\ubc88 \uad74\uc740 \uc778\uc811\ud574 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud604\uc7ac \uac01\uac01\uc758 \uad74\uc5d0\ub294 a<sub>i<\/sub> \ub9c8\ub9ac\uc758 \ub450\ub354\uc9c0\uac00 \uc788\uace0, \uc7ac\ud604\uc774\ub294 \ubaa8\ud615 \uad8c\ucd1d\uc73c\ub85c \uc774\ub4e4\uc744 \ucad3\uc544\ub0bc \uacc4\ud68d\uc774\ub2e4. \uc7ac\ud604\uc774\uac00 \ubaa8\ud615 \uad8c\ucd1d\uc744 \uc3f4\uc11c i\ubc88 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\uc5d0\uac8c \uac81\uc744 \uc8fc\uba74, \uadf8 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\ub4e4\uc774 \uac81\uc744 \uba39\uace0 \ub3c4\ub9dd\uac00\uac8c \ub41c\ub2e4. (\ubaa8\ud615\uc774\ub77c \uc8fd\uc9c0\ub294 \uc54a\ub294\ub2e4.) \ubfd0\ub9cc \uc544\ub2c8\ub77c, \uadf8 \uad74\uacfc \uc778\uc811\ud55c \uc591 \uc606 \ub450\uac1c\uc758 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\ub4e4\ub3c4 \uac81\uc744 \uba39\uc5b4\uc11c, \uc778\uc811\ud55c \uad74\ub85c \uc774\ub3d9\ud558\uac8c \ub41c\ub2e4. \ub2f9\uc5f0\ud788, \uc778\uc811\ud55c \uad74\uc774\ub77c \ud558\uba74 i\ubc88 \uad74\uc740 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, 10\ubc88 \uad74\uc5d0 \uac81\uc744 \uc92c\ub2e4\uba74, 10\ubc88 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\ub294 \ubaa8\ub450 \uad74\uc744 \ud0c8\ucd9c\ud558\uace0, 9\ubc88 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\ub294 8\ubc88 \uad74\ub85c \ub3c4\ub9dd\uac00\uace0, 11\ubc88 \uad74\uc5d0 \uc788\ub294 \ub450\ub354\uc9c0\ub294 12\ubc88 \uad74\ub85c \ub3c4\ub9dd\uac04\ub2e4.<\/p>\r\n\r\n<p>\uc7ac\ud604\uc774\ub294 3D \ud504\ub9b0\ud130\ub85c k\uac1c\uc758 \ucd1d\uc54c\uc744 \ub9cc\ub4e4\uc5c8\uace0, \ucd5c\ub300\ud55c \ub9ce\uc740 \ub450\ub354\uc9c0\ub97c \ucad3\uc544\ub0b4\uace0 \uc2f6\ub2e4. \ucd1d\uc744 k\ubc88 \uc774\ud558\ub85c \uc0ac\uc6a9\ud588\uc744 \ub54c, \ucd5c\ub300 \uba87 \ub9c8\ub9ac\uc758 \ub450\ub354\uc9c0\uac00 \uad74\uc744 \ud0c8\ucd9c\ud558\ub294\uac00?<\/p>\r\n","input":"<p>\uccab\ubc88\uc9f8 \uc904\uc5d0 \ub450\ub354\uc9c0\uad74\uc758 \uc218 n, \ucd1d\uc758 \ucd5c\ub300 \uc0ac\uc6a9 \uac00\ub2a5 \uc218 k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (5 &le; n &le; 2000, 1 &le; k &le; n)<\/p>\r\n\r\n<p>\uc774\ud6c4 n\uac1c\uc758 \uc815\uc218 a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>n<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; a<sub>i<\/sub> &le; 10<sup>6<\/sup>) i\ubc88\uc9f8 \uad74\uc5d0 a<sub>i<\/sub>\ub9c8\ub9ac\uc758 \ub450\ub354\uc9c0\uac00 \uc0b0\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","output":"<p>\ucd1d\uc744 k\ubc88 \uc774\ud558\ub85c \uc0ac\uc6a9\ud588\uc744 \ub54c, \ud0c8\ucd9c\uc2dc\ud0ac \uc218 \uc788\ub294 \ub450\ub354\uc9c0 \uc218\uc758 \ucd5c\ub313\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ucd08\uae30 \ub450\ub354\uc9c0 \uad74\uc758 \uc0c1\ud0dc\ub294 [6, 1, 5, 3, 4] \uc774\ub2e4.<\/p>\r\n\r\n<p>\uccab\ubc88\uc9f8\ub85c, \uc7ac\ud604\uc774\ub294 1\ubc88\uc9f8 \uad74\uc5d0 \ucd1d\uc744 \uc3f4\uc11c, 6\ub9c8\ub9ac\uc758 \ub450\ub354\uc9c0\ub97c \ud0c8\ucd9c\uc2dc\ud0a8\ub2e4. \ub450\ub354\uc9c0 \uad74\uc758 \uc0c1\ud0dc\ub294 [0, 0, 6, 7, 0]\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc81c, \uc7ac\ud604\uc774\ub294 4\ubc88\uc9f8 \uad74\uc5d0 \ucd1d\uc744 \uc3f4\uc11c, 7\ub9c8\ub9ac\uc758 \ub450\ub354\uc9c0\ub97c \ud0c8\ucd9c\uc2dc\ud0a8\ub2e4. \ucd1d 13\ub9c8\ub9ac\uac00 \ud0c8\ucd9c\ud55c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"7984","problem_lang":"1","title":"Rabbits","description":"<p>Byteasar has decided to grow lettuce in his garden. As you can imagine, Bytean rabbits simply love lettuce. So, not surprisingly, they instantly arrived in Byteasar&rsquo;s garden.<\/p>\r\n\r\n<p>In the garden there are n beds of lettuce numbered 1 through n. Every two subsequent beds are adjacent, that is, for each i = 1, 2, ..., n &minus; 1 the beds number i and i + 1 are adjacent and, moreover, the bed number n is adjacent to the bed number 1. Right now there are ai rabbits staying at the bed number i and eating away Byteasar&rsquo;s lettuce.<\/p>\r\n\r\n<p>Byteasar wants to chase out of the garden as many rabbits as possible. For this he is going to use his good old gun. The gun has k bullets inside. Rabbits are extremely timid, so whenever Byteasar shoots towards the bed number i, all the rabbits from that bed leave Byteasar&rsquo;s garden for good. What is more, the rabbits from both adjacent beds are so frightened that they all move to the adjacent bed (obviously, we mean the adjacent bed different from the one towards which was the shot).<\/p>\r\n\r\n<p>Help Byteasar to find the maximum number of rabbits that he can chase out of his garden with at most k shots.<\/p>\r\n","input":"<p>The first line of input contains two integers n and k (5 &le; n &le; 2000, 1 &le; k &le; n): the number of beds of lettuce in the garden and the number of bullets Byteasar has in his gun. The second line holds n integers a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>n<\/sub> (0 &le; a<sub>i<\/sub> &le; 1 000 000): the number of rabbits staying at the subsequent beds.<\/p>\r\n","output":"<p>Your program should output one integer: the maximum number of rabbits that can be chased out of Byteasar&rsquo;s garden using at most k shots.<\/p>\r\n","hint":"<p>Explanation of the example: First, Byteasar chases out the 6 rabbits from the bed number 1 (as a result, the rabbits from the bed number 5 move to the bed number 4, whereas the rabbits from the bed number 2 move to the bed number 3). Next, Byteasar chases out the 7 rabbits from the bed number 4.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]