문제
리듬게이머 코더빡은 최근 댄스 댄스 레볼루션(DDR)에 푹 빠져있다. 이 게임은 곡이 재생될 때 떨어지는 노트에 맞춰 발판을 밟는 게임으로, 많은 체력을 소모하기 때문에 체력 관리가 매우 중요하다.
곡은 $N$개의 구간으로 이루어져 있고, 어떠한 구간 $i$ $(1 \le i \le N)$에 대해 코더빡은 해당 구간을 플레이할지, 포기할지 선택할 수 있다. 해당 구간을 플레이할 때 얻을 수 있는 점수는 $s_i$점이며, 체력을 $h_i$만큼 소모한다. 구간을 포기할 때는, 점수를 얻지 못하고 체력도 소모하지 않는다.
곡이 시작할 때, 코더빡은 체력 100ドル$을 가지고 시작한다. 매 구간에 진입하기 전에 체력을 $K$만큼 회복한다. 이 체력 회복은 구간을 플레이하거나 포기하는 것과는 무관하게 일어남에 유의하라. 회복 후 코더빡의 체력이 100ドル$을 초과하는 경우 체력이 100ドル$이 되며, 구간을 플레이했을 때 체력이 0ドル$ 미만으로 하락하는 경우 코더빡은 해당 구간을 포기해야만 한다.
하루 종일 DDR을 밟아 기진맥진인 코더빡은 더 이상 체력 관리를 위한 판단을 내릴 수 없다. 코더빡이 성과를 뽑아낼 수 있도록 그가 얻을 수 있는 최대 점수를 알려주는 프로그램을 작성하시오.
지문에서 언급하지 않은 게임오버 등의 시스템은 이 문제에서 고려하지 않는다.
출력
코더빡이 얻을 수 있는 최대 점수를 출력한다.
세 구간 이상을 플레이하는 방법은 없다. 90ドル$점짜리 구간을 플레이한 후 체력이 40ドル$이 되며, 1ドル$개의 구간을 포기하고 체력을 2ドル$번 회복해 100ドル$점짜리 구간을 플레이하는 방법으로 최대 점수인 190ドル$점을 얻을 수 있다.
[{"problem_id":"29756","problem_lang":"0","title":"DDR \uccb4\ub825 \uad00\ub9ac","description":"<p>\ub9ac\ub4ec\uac8c\uc774\uba38 \ucf54\ub354\ube61\uc740 \ucd5c\uadfc \ub304\uc2a4 \ub304\uc2a4 \ub808\ubcfc\ub8e8\uc158(DDR)\uc5d0 \ud479 \ube60\uc838\uc788\ub2e4. \uc774 \uac8c\uc784\uc740 \uace1\uc774 \uc7ac\uc0dd\ub420 \ub54c \ub5a8\uc5b4\uc9c0\ub294 \ub178\ud2b8\uc5d0 \ub9de\ucdb0 \ubc1c\ud310\uc744 \ubc1f\ub294 \uac8c\uc784\uc73c\ub85c, \ub9ce\uc740 \uccb4\ub825\uc744 \uc18c\ubaa8\ud558\uae30 \ub54c\ubb38\uc5d0 \uccb4\ub825 \uad00\ub9ac\uac00 \ub9e4\uc6b0 \uc911\uc694\ud558\ub2e4.<\/p>\r\n\r\n<p>\uace1\uc740 $N$\uac1c\uc758 \uad6c\uac04\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uc5b4\ub5a0\ud55c \uad6c\uac04 $i$ $(1 \\le i \\le N)$\uc5d0 \ub300\ud574 \ucf54\ub354\ube61\uc740 \ud574\ub2f9 \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud560\uc9c0, \ud3ec\uae30\ud560\uc9c0 \uc120\ud0dd\ud560 \uc218 \uc788\ub2e4. \ud574\ub2f9 \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud560 \ub54c \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\ub294 $s_i$\uc810\uc774\uba70, \uccb4\ub825\uc744 $h_i$\ub9cc\ud07c \uc18c\ubaa8\ud55c\ub2e4. \uad6c\uac04\uc744 \ud3ec\uae30\ud560 \ub54c\ub294, \uc810\uc218\ub97c \uc5bb\uc9c0 \ubabb\ud558\uace0 \uccb4\ub825\ub3c4 \uc18c\ubaa8\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uace1\uc774 \uc2dc\uc791\ud560 \ub54c, \ucf54\ub354\ube61\uc740 \uccb4\ub825 $100$\uc744 \uac00\uc9c0\uace0 \uc2dc\uc791\ud55c\ub2e4. \ub9e4 \uad6c\uac04\uc5d0 \uc9c4\uc785\ud558\uae30 \uc804\uc5d0 \uccb4\ub825\uc744 $K$\ub9cc\ud07c \ud68c\ubcf5\ud55c\ub2e4. \uc774 \uccb4\ub825 \ud68c\ubcf5\uc740 \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud558\uac70\ub098 \ud3ec\uae30\ud558\ub294 \uac83\uacfc\ub294 \ubb34\uad00\ud558\uac8c \uc77c\uc5b4\ub0a8\uc5d0 \uc720\uc758\ud558\ub77c. \ud68c\ubcf5 \ud6c4 \ucf54\ub354\ube61\uc758 \uccb4\ub825\uc774 $100$\uc744 \ucd08\uacfc\ud558\ub294 \uacbd\uc6b0 \uccb4\ub825\uc774 $100$\uc774 \ub418\uba70, \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud588\uc744 \ub54c \uccb4\ub825\uc774 $0$ \ubbf8\ub9cc\uc73c\ub85c \ud558\ub77d\ud558\ub294 \uacbd\uc6b0 \ucf54\ub354\ube61\uc740 \ud574\ub2f9 \uad6c\uac04\uc744 \ud3ec\uae30\ud574\uc57c\ub9cc \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud558\ub8e8 \uc885\uc77c DDR\uc744 \ubc1f\uc544 \uae30\uc9c4\ub9e5\uc9c4\uc778 \ucf54\ub354\ube61\uc740 \ub354 \uc774\uc0c1 \uccb4\ub825 \uad00\ub9ac\ub97c \uc704\ud55c \ud310\ub2e8\uc744 \ub0b4\ub9b4 \uc218 \uc5c6\ub2e4. \ucf54\ub354\ube61\uc774 \uc131\uacfc\ub97c \ubf51\uc544\ub0bc \uc218 \uc788\ub3c4\ub85d \uadf8\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc810\uc218\ub97c \uc54c\ub824\uc8fc\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc9c0\ubb38\uc5d0\uc11c \uc5b8\uae09\ud558\uc9c0 \uc54a\uc740 \uac8c\uc784\uc624\ubc84 \ub4f1\uc758 \uc2dc\uc2a4\ud15c\uc740 \uc774 \ubb38\uc81c\uc5d0\uc11c \uace0\ub824\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc815\uc218 $N$\uacfc $K$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $N$\uc740 \uace1\uc758 \uc804\uccb4 \uad6c\uac04\uc758 \uc218\ub97c \uc758\ubbf8\ud558\uba70, $K$\ub294 \ud68c\ubcf5\ud558\ub294 \uccb4\ub825\uc758 \uc591\uc774\ub2e4. $(1 \\leq N \\leq 1\\,000;$ $1 \\leq K \\leq 10)$<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc815\uc218 $s_1$, $s_2$, $\\cdots$, $s_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\leq s_i \\leq 1\\,000)$<\/p>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc815\uc218 $h_1$, $h_2$, $\\cdots$, $h_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\leq h_i \\leq 100)$<\/p>\r\n","output":"<p>\ucf54\ub354\ube61\uc774 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc810\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>\ubaa8\ub4e0 \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","sample_explain_2":"<p>\uc138 \uad6c\uac04 \uc774\uc0c1\uc744 \ud50c\ub808\uc774\ud558\ub294 \ubc29\ubc95\uc740 \uc5c6\ub2e4. $90$\uc810\uc9dc\ub9ac \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud55c \ud6c4 \uccb4\ub825\uc774 $40$\uc774 \ub418\uba70, $1$\uac1c\uc758 \uad6c\uac04\uc744 \ud3ec\uae30\ud558\uace0 \uccb4\ub825\uc744 $2$\ubc88 \ud68c\ubcf5\ud574 $100$\uc810\uc9dc\ub9ac \uad6c\uac04\uc744 \ud50c\ub808\uc774\ud558\ub294 \ubc29\ubc95\uc73c\ub85c \ucd5c\ub300 \uc810\uc218\uc778&nbsp;$190$\uc810\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n"},{"problem_id":"29756","problem_lang":"1","title":"DDR Stamina Management","description":"<p>Koderpark, a rhythm gamer, is currently engrossed in Dance Dance Revolution (DDR). Players step on the panels in time with the falling arrows in this game. Since it requires a significant amount of stamina, managing stamina is crucial.<\/p>\r\n\r\n<p>A song consists of $N$ sections, and for any given section $i$ (where $1 \\le i&nbsp;\\le N$), Koderpark can choose to play or skip that section. When he decides to play a section, he can earn $s_i$\u200b points but will also consume $h_i$\u200b stamina. If he skips a section, he doesn&#39;t earn any points and doesn&#39;t consume any stamina.<\/p>\r\n\r\n<p>At the start of a song, Koderpark begins with $100$ stamina. Before entering each section, he recovers $K$ stamina. This stamina recovery happens regardless of whether Koderpark plays or skips the section. After recovery, if Koderpark&#39;s stamina exceeds $100$,&nbsp;it&#39;s reset to $100$. If, after playing a section, his stamina drops below $0$, he must skip that section.<\/p>\r\n\r\n<p>Having played DDR all day and utterly exhausted, Koderpark can no longer decide how to manage his stamina. Write a program to get the maximum score Koderpark can achieve.<\/p>\r\n\r\n<p>Systems not mentioned in the description, like &quot;game over,&quot; are not considered in this problem.<\/p>\r\n","input":"\r\n<p>The first line contains two integers, the total number of sections in the song $N$ and the amount of stamina recovered $K$, separated by a space. $(1 \\leq N \\leq 1\\,000;$ $1 \\leq K \\leq 10)$<\/p>\r\n\r\n<p>The second line contains&nbsp;the integers&nbsp;$s_1$, $s_2$, $\\cdots$, $s_N$\u200b, separated by spaces. $(1 \\leq s_i&nbsp;\\leq 1\\,000)$<\/p>\r\n\r\n<p>The third line contains the integers $h_1$, $h_2$, $\\cdots$, $h_N$, separated by spaces. $(1 \\leq h_i&nbsp;\\leq 100)$<\/p>\r\n","output":"<p>Print the maximum score Koderpark can achieve.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p>He can play all the sections.<\/p>\r\n","sample_explain_2":"<p>There is no method to play more than two sections. After playing the $90$-point section, the stamina becomes $40$. By skipping one section and recovering stamina twice, Koderpark can then play the $100$-point section, achieving a maximum score of $190$ points.<\/p>\r\n"}]