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문제

리듬게임 국가대표, 월드컵 준결승의 주역인 고인물 카루나는 리듬게임을 제패하기 위해 새로운 리듬게임을 시작했다. 이 게임은 굉장히 특이한 점수 체계를 가지고 있다.

이 게임은 콤보라는 시스템을 가지고 있다. 잘 모를 수도 있는 사람들을 위해 설명하자면, 곡이 시작할 때의 콤보는 0이고, 각 노트마다 노트를 치면 콤보가 1 증가하고, 노트를 치지 못하면 콤보가 끊기며 0으로 돌아간다. 먼저 나온 노트를 치거나 놓치기 전에는 그 노트를 칠 수 없다.

점수의 계산은 각 노트에 대한 점수 Ai와 콤보에 대한 점수 Cj, 콤보가 끊길 때의 점수 P에 따라 계산된다. 콤보가 클수록 콤보에 대한 점수 Cj는 작아지며, i번째 노트를 친 후에 콤보가 j가 된다면 Ai × Cj점을 얻는다. 만약 노트를 치지 못했다면 그 노트에 대한 점수는 없다. 

또한, 노트를 놓치거나 곡이 끝나서 콤보가 끊길 때마다 P점을 추가로 얻는다. 즉, 콤보가 1 이상에서 0으로 바뀌거나 곡이 끝날 때 콤보가 1 이상일 경우 점수를 얻는다.

카루나는 엄청난 고인물이기 때문에 곡과는 상관 없이 최대 K개의 노트를 골라서 칠 수 있다. 즉, 노트가 K개 이하라면 아무 노트나 선택해서 원하는 대로 칠 수 있다.

카루나가 칠 곡의 정보가 주어질 때, 얻을 수 있는 최대 점수를 구해 주자!

입력

첫째 줄에는 세 정수 N, K, P가 공백으로 구분되어 주어진다. N은 곡에 있는 노트의 수를 의미한다.

둘째 줄에는 N개의 정수가 공백으로 구분되어 주어진다. i번째의 수는 i번째 노트에 대한 점수 Ai를 의미한다.

셋째 줄에는 N개의 정수가 공백으로 구분되어 주어진다. j번째의 수는 콤보 j에 대한 점수 Cj를 의미한다.

출력

카루나가 얻을 수 있는 점수의 최댓값을 출력한다. 

제한

  • 1 ≤ N, K ≤ 2,000
  • -109 ≤ P ​≤ 109
  • 0 ≤ Ai ≤ 105
  • -105 ≤ Cj ≤ 105
  • 1 ≤ j ≤ N-1를 만족하는 모든 정수 j에 대해, Cj ≥ Cj+1임이 보장된다.

예제 입력 1

5 5 1
5 4 3 2 1
5 4 3 2 1

예제 출력 1

57

1번째, 2번째, 4번째, 5번째 노트를 치게 되면 카루나가 얻게 되는 점수는 5×5+4×4+1+2×5+1×4+1=57점을 얻을 수 있으며, 더 높은 점수를 얻는 것은 불가능하다.

[{"problem_id":"18942","problem_lang":"0","title":"\uace0\uc778\ubb3c\uc758 \uc0c8\ub85c\uc6b4 \ub9ac\ub4ec\uac8c\uc784","description":"<p>\ub9ac\ub4ec\uac8c\uc784 \uad6d\uac00\ub300\ud45c, \uc6d4\ub4dc\ucef5 \uc900\uacb0\uc2b9\uc758 \uc8fc\uc5ed\uc778 \uace0\uc778\ubb3c \uce74\ub8e8\ub098\ub294 \ub9ac\ub4ec\uac8c\uc784\uc744 \uc81c\ud328\ud558\uae30 \uc704\ud574 \uc0c8\ub85c\uc6b4 \ub9ac\ub4ec\uac8c\uc784\uc744 \uc2dc\uc791\ud588\ub2e4. \uc774 \uac8c\uc784\uc740 \uad49\uc7a5\ud788 \ud2b9\uc774\ud55c \uc810\uc218 \uccb4\uacc4\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uac8c\uc784\uc740 \ucf64\ubcf4\ub77c\ub294 \uc2dc\uc2a4\ud15c\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4. \uc798 \ubaa8\ub97c \uc218\ub3c4 \uc788\ub294 \uc0ac\ub78c\ub4e4\uc744 \uc704\ud574 \uc124\uba85\ud558\uc790\uba74, \uace1\uc774 \uc2dc\uc791\ud560 \ub54c\uc758 \ucf64\ubcf4\ub294 0\uc774\uace0, \uac01 \ub178\ud2b8\ub9c8\ub2e4 \ub178\ud2b8\ub97c \uce58\uba74 \ucf64\ubcf4\uac00 1 \uc99d\uac00\ud558\uace0, \ub178\ud2b8\ub97c \uce58\uc9c0 \ubabb\ud558\uba74 \ucf64\ubcf4\uac00 \ub04a\uae30\uba70 0\uc73c\ub85c \ub3cc\uc544\uac04\ub2e4. \uba3c\uc800 \ub098\uc628&nbsp;\ub178\ud2b8\ub97c \uce58\uac70\ub098 \ub193\uce58\uae30 \uc804\uc5d0\ub294 \uadf8 \ub178\ud2b8\ub97c \uce60 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc810\uc218\uc758 \uacc4\uc0b0\uc740&nbsp;\uac01 \ub178\ud2b8\uc5d0 \ub300\ud55c \uc810\uc218&nbsp;<em>A<sub>i<\/sub><\/em>\uc640&nbsp;\ucf64\ubcf4\uc5d0&nbsp;\ub300\ud55c&nbsp;\uc810\uc218 <em>C<sub>j<\/sub><\/em>, \ucf64\ubcf4\uac00 \ub04a\uae38 \ub54c\uc758 \uc810\uc218 <em>P<\/em>\uc5d0 \ub530\ub77c \uacc4\uc0b0\ub41c\ub2e4. \ucf64\ubcf4\uac00 \ud074\uc218\ub85d \ucf64\ubcf4\uc5d0 \ub300\ud55c \uc810\uc218 <em>C<sub>j<\/sub><\/em>\ub294 \uc791\uc544\uc9c0\uba70,&nbsp;<em>i<\/em>\ubc88\uc9f8 \ub178\ud2b8\ub97c \uce5c \ud6c4\uc5d0&nbsp;\ucf64\ubcf4\uac00&nbsp;<em>j<\/em>\uac00 \ub41c\ub2e4\uba74 <em>A<sub>i<\/sub><\/em> &times; <em>C<sub>j<\/sub><\/em>\uc810\uc744 \uc5bb\ub294\ub2e4. \ub9cc\uc57d&nbsp;\ub178\ud2b8\ub97c \uce58\uc9c0 \ubabb\ud588\ub2e4\uba74 \uadf8 \ub178\ud2b8\uc5d0 \ub300\ud55c \uc810\uc218\ub294 \uc5c6\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ub610\ud55c, \ub178\ud2b8\ub97c \ub193\uce58\uac70\ub098 \uace1\uc774 \ub05d\ub098\uc11c \ucf64\ubcf4\uac00 \ub04a\uae38 \ub54c\ub9c8\ub2e4 <em>P<\/em>\uc810\uc744 \ucd94\uac00\ub85c \uc5bb\ub294\ub2e4. \uc989, \ucf64\ubcf4\uac00 1 \uc774\uc0c1\uc5d0\uc11c&nbsp;0\uc73c\ub85c \ubc14\ub00c\uac70\ub098 \uace1\uc774 \ub05d\ub0a0 \ub54c \ucf64\ubcf4\uac00 1 \uc774\uc0c1\uc77c \uacbd\uc6b0 \uc810\uc218\ub97c \uc5bb\ub294\ub2e4.<\/p>\r\n\r\n<p>\uce74\ub8e8\ub098\ub294 \uc5c4\uccad\ub09c \uace0\uc778\ubb3c\uc774\uae30 \ub54c\ubb38\uc5d0 \uace1\uacfc\ub294 \uc0c1\uad00 \uc5c6\uc774&nbsp;\ucd5c\ub300<em> K<\/em>\uac1c\uc758 \ub178\ud2b8\ub97c \uace8\ub77c\uc11c \uce60 \uc218 \uc788\ub2e4. \uc989, \ub178\ud2b8\uac00 <em>K<\/em>\uac1c \uc774\ud558\ub77c\uba74 \uc544\ubb34 \ub178\ud2b8\ub098 \uc120\ud0dd\ud574\uc11c \uc6d0\ud558\ub294 \ub300\ub85c \uce60 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uce74\ub8e8\ub098\uac00 \uce60 \uace1\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc810\uc218\ub97c \uad6c\ud574 \uc8fc\uc790!<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \uc138 \uc815\uc218 <em>N<\/em>, <em>K,<\/em>&nbsp;<em>P<\/em>\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. <em>N<\/em>\uc740&nbsp;\uace1\uc5d0 \uc788\ub294&nbsp;\ub178\ud2b8\uc758 \uc218\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 <em>N<\/em>\uac1c\uc758 \uc815\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. <em>i<\/em>\ubc88\uc9f8\uc758 \uc218\ub294&nbsp;<em>i<\/em>\ubc88\uc9f8 \ub178\ud2b8\uc5d0 \ub300\ud55c \uc810\uc218 <i>A<sub>i<\/sub><\/i>\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0\ub294 <em>N<\/em>\uac1c\uc758 \uc815\uc218\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. <em>j<\/em>\ubc88\uc9f8\uc758 \uc218\ub294&nbsp;\ucf64\ubcf4 <i>j<\/i>\uc5d0 \ub300\ud55c \uc810\uc218 <em>C<sub>j<\/sub><\/em>\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uce74\ub8e8\ub098\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\uc758 \ucd5c\ub313\uac12\uc744&nbsp;\ucd9c\ub825\ud55c\ub2e4.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>1 &le; <em>N, K&nbsp;<\/em>&le; 2,000<\/li>\r\n\t<li>-10<sup>9<\/sup>&nbsp;&le;&nbsp;<em>P <\/em>\u200b&le; 10<sup>9<\/sup><\/li>\r\n\t<li>0 &le;&nbsp;<em>A<sub>i<\/sub><\/em>&nbsp;&le; 10<sup>5<\/sup><\/li>\r\n\t<li>-10<sup>5<\/sup> &le;&nbsp;<em>C<\/em><sub><em>j<\/em><\/sub>&nbsp;&le; 10<sup>5<\/sup><\/li>\r\n\t<li>1 &le;&nbsp;<em>j<\/em>&nbsp;&le;&nbsp;<em>N<\/em>-1\ub97c&nbsp;\ub9cc\uc871\ud558\ub294 \ubaa8\ub4e0 \uc815\uc218&nbsp;<em>j<\/em>\uc5d0 \ub300\ud574, <em>C<sub>j<\/sub><\/em>&nbsp;&ge;&nbsp;<em>C<sub>j+1<\/sub><\/em>\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>1\ubc88\uc9f8, 2\ubc88\uc9f8, 4\ubc88\uc9f8, 5\ubc88\uc9f8 \ub178\ud2b8\ub97c&nbsp;\uce58\uac8c \ub418\uba74 \uce74\ub8e8\ub098\uac00 \uc5bb\uac8c \ub418\ub294 \uc810\uc218\ub294 5&times;5+4&times;4+1+2&times;5+1&times;4+1=57\uc810\uc744 \uc5bb\uc744 \uc218 \uc788\uc73c\uba70, \ub354 \ub192\uc740 \uc810\uc218\ub97c \uc5bb\ub294 \uac83\uc740 \ubd88\uac00\ub2a5\ud558\ub2e4.<\/p>\r\n"},{"problem_id":"18942","problem_lang":"1","title":"Rhythm Game","description":"<p>The famous artist Karuna is playing the rhythm gane.<\/p>\r\n\r\n<p>The artist is trying to hit the notes in a song. The song is a sequence of $N$ notes.<\/p>\r\n\r\n<p>The scoring system used in this game is as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>At beginning of the song (before first note), the score is $0$ and combo&nbsp;bonus is $0$.<\/li>\r\n\t<li>Each note has its own cost. The cost of $i$-th note is $A_i$.&nbsp;<\/li>\r\n\t<li>The combo bonus value is equal to $0$ if Karuna misses current note, or $C_j$ if Karuna hits this note and there are $j$ notes in a row which Karuna hits.<\/li>\r\n\t<li>If Karuna hits the $i$-th note and the combo length after that is $j$, the value of $A_i \\cdot C_j$ is added to the score.<\/li>\r\n\t<li>If Karuna misses the note, the length of the combo is reset to $0$. If it was non-zero before (in other words, if Karuna hit the previous note), then the combo ending score $P$ is added to the score.<\/li>\r\n\t<li>If Karuna hits the last note in the song, the combo ending score $P$ is added to the score as well.<\/li>\r\n<\/ul>\r\n\r\n<p>Karuna&#39;s skills allow him to hit no more than $K$ notes during the song. For every note, he may choose to hit it or to miss it, as long as he hits no more than $K$ notes in total.<\/p>\r\n\r\n<p>Given all the parameters, tell the maximum score Karuna can get.<\/p>\r\n","input":"<p>The first line of the input contains three integers $N$, $K$ and $P$ ($1 \\le N, K \\le 2000$, $-10^9 \\le P \\le 10^9$): the number of notes in the song, the maximum number of notes Karuna can hit and combo break score, respectively.<\/p>\r\n\r\n<p>The second line contains $N$ integers separated by spaces. The $i$-th number represents the score $A_i$ for hitting the $i$-th note ($0 \\le A_i \\le 10^5$).<\/p>\r\n\r\n<p>The third line contains $N$ integers separated by spaces. The $j$-th number represents the score $C_j$ for a combo of length $j$ ($-10^5 \\le C_j \\le 10^5$, and for all $1 \\le j \\le N-1$, it is guaranteed that $C_j \\ge C_{j+1}$).<\/p>\r\n","output":"<p>Print one integer: the maximum score Karuna can get in the Rhythm Game.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]