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문제

카오는 오랫동안 메이플스토리를 플레이하며 $N$개의 캐릭터를 육성하였다.

지속적인 스펙업을 위해 꾸준하게 메소를 벌어야 할 필요성을 느낀 카오는, 지금까지 키워온 캐릭터들을 활용하여 메소를 벌기로 하였다. 여러 캐릭터로 보스를 효율적으로 잡기 위해, 하루에 한 캐릭터 당 최대 $15$분씩, 최대 $M$개의 캐릭터만 보스를 잡기로 하였다.

캐릭터가 보스에게 데미지를 넣으면 보스의 체력이 데미지만큼 감소하며, 보스의 체력이 $0$ 이하가 되면 보스를 잡게 된다. 데미지의 계산은 매초 이루어지기 때문에, $1$초 미만의 시간 동안 적용된 데미지는 보스에게 적용되지 않는다.

캐릭터마다 주어진 $15$분 동안은 매초 일정한 데미지를 넣을 수 있으며, 보스를 잡은 후 다른 보스를 잡으러 떠나는 시간은 계산하지 않는다. 캐릭터마다 각 보스는 $1$회씩만 처치할 수 있으며, 다른 캐릭터가 잡은 보스라도, 현재 캐릭터가 잡지 않은 보스라면 잡을 수 있다. 보스를 잡던 도중 캐릭터를 변경하는 것은 불가능하며, 캐릭터가 상대하는 보스의 체력은 공유되지 않아, 오롯이 한 캐릭터의 힘으로 보스를 상대해야 한다.

보스 몬스터의 체력, 보상 메소 정보와 캐릭터의 데미지 정보가 주어질 때, 카오가 계획에 맞추어 하루에 보스를 잡아 얻을 수 있는 최대 메소를 구해보자.

입력

첫 줄에는 보유한 캐릭터의 개수 $N$, 하루에 사용할 캐릭터의 개수 $M$, 보스의 가짓수 $K$가 공백으로 구분되어 주어진다. $(1 \le M \le N \le 49;$ $1 \le K \le 13)$

그다음 $N$줄에 걸쳐서 캐릭터가 $1$초에 가하는 데미지 $D$가 주어진다. $(1 \le D \le 10^{11})$

그다음 $K$줄에 걸쳐서 보스의 체력 $P$와 보스를 처치했을 때 드랍하는 메소 $Q$가 공백으로 구분되어 주어진다. $(1 \le P \le 2.66 \times 10^{11};$ $1 \le Q \le 1\,596\,506)$

입력으로 들어오는 모든 수는 정수임이 보장된다.

출력

카오가 계획에 맞추어 보스를 잡았을 때, 하루에 보스를 잡아 얻을 수 있는 최대 메소를 출력한다.

예제 입력 1

3 2 3
1
2
3
900 30
1800 40
2700 50

예제 출력 1

110

다음 경우에 $110$메소를 획득할 수 있다.

  • $2$번째 캐릭터로 $15$분에 걸쳐 $2$번째 보스를 잡아 $40$메소 획득
  • $3$번째 캐릭터로 $5$분에 걸쳐 $1$번째 보스를 잡아 $30$메소 획득
  • $3$번째 캐릭터로 $10$분에 걸쳐 $2$번째 보스를 잡아 $40$메소 획득

예제 입력 2

2 2 3
10
20
8999 10
17999 100
1 1

예제 출력 2

110

다음 경우에 $110$메소를 획득할 수 있다.

  • $1$번째 캐릭터로 $15$분에 걸쳐 $1$번째 보스를 잡아 $10$메소 획득
  • $2$번째 캐릭터로 $15$분에 걸쳐 $2$번째 보스를 잡아 $100$메소 획득

$1$번째 캐릭터가 $14$분 $59$초 동안 넣을 수 있는 데미지는 $8\,990$이다. 남은 시간 $1$초 동안 $1$번째 보스와 $3$번째 보스를 모두 잡을 수 없어, 위와 같은 결과가 나오게 된다.

노트

보스의 체력 $P$의 제한 $2.66 \times 10^{11}$와 드랍하는 메소 $Q$의 제한 $1\,596\,506$은 2023년 8월 10일 업데이트 이전의 가장 많은 체력(카오스 혼테일)과 결정의 가격(노멀 파풀라투스)을 가진 일간 보스의 정보이다.

[{"problem_id":"29792","problem_lang":"0","title":"\uaddc\uce59\uc801\uc778 \ubcf4\uc2a4\ub3cc\uc774","description":"<p>\uce74\uc624\ub294 \uc624\ub7ab\ub3d9\uc548 \uba54\uc774\ud50c\uc2a4\ud1a0\ub9ac\ub97c \ud50c\ub808\uc774\ud558\uba70 $N$\uac1c\uc758 \uce90\ub9ad\ud130\ub97c \uc721\uc131\ud558\uc600\ub2e4.<\/p>\r\n\r\n<p>\uc9c0\uc18d\uc801\uc778 \uc2a4\ud399\uc5c5\uc744 \uc704\ud574 \uafb8\uc900\ud558\uac8c \uba54\uc18c\ub97c \ubc8c\uc5b4\uc57c \ud560 \ud544\uc694\uc131\uc744 \ub290\ub080 \uce74\uc624\ub294, \uc9c0\uae08\uae4c\uc9c0 \ud0a4\uc6cc\uc628 \uce90\ub9ad\ud130\ub4e4\uc744 \ud65c\uc6a9\ud558\uc5ec \uba54\uc18c\ub97c \ubc8c\uae30\ub85c \ud558\uc600\ub2e4. \uc5ec\ub7ec \uce90\ub9ad\ud130\ub85c \ubcf4\uc2a4\ub97c \ud6a8\uc728\uc801\uc73c\ub85c \uc7a1\uae30 \uc704\ud574, \ud558\ub8e8\uc5d0 \ud55c \uce90\ub9ad\ud130 \ub2f9 \ucd5c\ub300 $15$\ubd84\uc529, \ucd5c\ub300 $M$\uac1c\uc758 \uce90\ub9ad\ud130\ub9cc \ubcf4\uc2a4\ub97c \uc7a1\uae30\ub85c \ud558\uc600\ub2e4.<\/p>\r\n\r\n<p>\uce90\ub9ad\ud130\uac00 \ubcf4\uc2a4\uc5d0\uac8c \ub370\ubbf8\uc9c0\ub97c \ub123\uc73c\uba74 \ubcf4\uc2a4\uc758 \uccb4\ub825\uc774 \ub370\ubbf8\uc9c0\ub9cc\ud07c \uac10\uc18c\ud558\uba70, \ubcf4\uc2a4\uc758 \uccb4\ub825\uc774 $0$ \uc774\ud558\uac00 \ub418\uba74 \ubcf4\uc2a4\ub97c \uc7a1\uac8c \ub41c\ub2e4. \ub370\ubbf8\uc9c0\uc758 \uacc4\uc0b0\uc740 \ub9e4\ucd08 \uc774\ub8e8\uc5b4\uc9c0\uae30 \ub54c\ubb38\uc5d0, $1$\ucd08 \ubbf8\ub9cc\uc758 \uc2dc\uac04 \ub3d9\uc548 \uc801\uc6a9\ub41c \ub370\ubbf8\uc9c0\ub294 \ubcf4\uc2a4\uc5d0\uac8c \uc801\uc6a9\ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uce90\ub9ad\ud130\ub9c8\ub2e4 \uc8fc\uc5b4\uc9c4 $15$\ubd84 \ub3d9\uc548\uc740 \ub9e4\ucd08 \uc77c\uc815\ud55c \ub370\ubbf8\uc9c0\ub97c \ub123\uc744 \uc218 \uc788\uc73c\uba70, \ubcf4\uc2a4\ub97c \uc7a1\uc740 \ud6c4 \ub2e4\ub978 \ubcf4\uc2a4\ub97c \uc7a1\uc73c\ub7ec \ub5a0\ub098\ub294 \uc2dc\uac04\uc740 \uacc4\uc0b0\ud558\uc9c0 \uc54a\ub294\ub2e4. \uce90\ub9ad\ud130\ub9c8\ub2e4 \uac01 \ubcf4\uc2a4\ub294 $1$\ud68c\uc529\ub9cc \ucc98\uce58\ud560 \uc218 \uc788\uc73c\uba70, \ub2e4\ub978 \uce90\ub9ad\ud130\uac00 \uc7a1\uc740 \ubcf4\uc2a4\ub77c\ub3c4, \ud604\uc7ac \uce90\ub9ad\ud130\uac00 \uc7a1\uc9c0 \uc54a\uc740 \ubcf4\uc2a4\ub77c\uba74 \uc7a1\uc744 \uc218 \uc788\ub2e4. \ubcf4\uc2a4\ub97c \uc7a1\ub358 \ub3c4\uc911 \uce90\ub9ad\ud130\ub97c \ubcc0\uacbd\ud558\ub294 \uac83\uc740 \ubd88\uac00\ub2a5\ud558\uba70, \uce90\ub9ad\ud130\uac00 \uc0c1\ub300\ud558\ub294 \ubcf4\uc2a4\uc758 \uccb4\ub825\uc740 \uacf5\uc720\ub418\uc9c0 \uc54a\uc544, \uc624\ub86f\uc774 \ud55c \uce90\ub9ad\ud130\uc758 \ud798\uc73c\ub85c \ubcf4\uc2a4\ub97c \uc0c1\ub300\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubcf4\uc2a4 \ubaac\uc2a4\ud130\uc758 \uccb4\ub825, \ubcf4\uc0c1 \uba54\uc18c \uc815\ubcf4\uc640 \uce90\ub9ad\ud130\uc758 \ub370\ubbf8\uc9c0 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, \uce74\uc624\uac00 \uacc4\ud68d\uc5d0 \ub9de\ucd94\uc5b4 \ud558\ub8e8\uc5d0 \ubcf4\uc2a4\ub97c \uc7a1\uc544 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uba54\uc18c\ub97c \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0\ub294 \ubcf4\uc720\ud55c \uce90\ub9ad\ud130\uc758 \uac1c\uc218 $N$, \ud558\ub8e8\uc5d0 \uc0ac\uc6a9\ud560 \uce90\ub9ad\ud130\uc758 \uac1c\uc218 $M$, \ubcf4\uc2a4\uc758 \uac00\uc9d3\uc218 $K$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le M \\le N \\le 49;$ $1 \\le K \\le 13)$<\/p>\r\n\r\n<p>\uadf8\ub2e4\uc74c $N$\uc904\uc5d0 \uac78\uccd0\uc11c \uce90\ub9ad\ud130\uac00 $1$\ucd08\uc5d0 \uac00\ud558\ub294 \ub370\ubbf8\uc9c0 $D$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le D \\le 10^{11})$<\/p>\r\n\r\n<p>\uadf8\ub2e4\uc74c $K$\uc904\uc5d0 \uac78\uccd0\uc11c \ubcf4\uc2a4\uc758 \uccb4\ub825 $P$\uc640 \ubcf4\uc2a4\ub97c \ucc98\uce58\ud588\uc744 \ub54c \ub4dc\ub78d\ud558\ub294 \uba54\uc18c $Q$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le P \\le 2.66 \\times 10^{11};$ $1 \\le Q \\le 1\\,596\\,506)$<\/p>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c \ub4e4\uc5b4\uc624\ub294 \ubaa8\ub4e0 \uc218\ub294 \uc815\uc218\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","output":"<p>\uce74\uc624\uac00 \uacc4\ud68d\uc5d0 \ub9de\ucd94\uc5b4 \ubcf4\uc2a4\ub97c \uc7a1\uc558\uc744 \ub54c, \ud558\ub8e8\uc5d0 \ubcf4\uc2a4\ub97c \uc7a1\uc544 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uba54\uc18c\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ubcf4\uc2a4\uc758 \uccb4\ub825 $P$\uc758 \uc81c\ud55c $2.66 \\times 10^{11}$\uc640 \ub4dc\ub78d\ud558\ub294 \uba54\uc18c $Q$\uc758 \uc81c\ud55c $1\\,596\\,506$\uc740 2023\ub144 8\uc6d4 10\uc77c \uc5c5\ub370\uc774\ud2b8 \uc774\uc804\uc758 \uac00\uc7a5 \ub9ce\uc740 \uccb4\ub825(\uce74\uc624\uc2a4 \ud63c\ud14c\uc77c)\uacfc \uacb0\uc815\uc758 \uac00\uaca9(\ub178\uba40 \ud30c\ud480\ub77c\ud22c\uc2a4)\uc744 \uac00\uc9c4 \uc77c\uac04 \ubcf4\uc2a4\uc758 \uc815\ubcf4\uc774\ub2e4.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>\ub2e4\uc74c \uacbd\uc6b0\uc5d0 $110$\uba54\uc18c\ub97c \ud68d\ub4dd\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$2$\ubc88\uc9f8 \uce90\ub9ad\ud130\ub85c $15$\ubd84\uc5d0 \uac78\uccd0 $2$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \uc7a1\uc544 $40$\uba54\uc18c \ud68d\ub4dd<\/li>\r\n\t<li>$3$\ubc88\uc9f8 \uce90\ub9ad\ud130\ub85c $5$\ubd84\uc5d0 \uac78\uccd0 $1$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \uc7a1\uc544 $30$\uba54\uc18c \ud68d\ub4dd<\/li>\r\n\t<li>$3$\ubc88\uc9f8 \uce90\ub9ad\ud130\ub85c $10$\ubd84\uc5d0 \uac78\uccd0 $2$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \uc7a1\uc544 $40$\uba54\uc18c \ud68d\ub4dd<\/li>\r\n<\/ul>\r\n","sample_explain_2":"<p>\ub2e4\uc74c \uacbd\uc6b0\uc5d0 $110$\uba54\uc18c\ub97c \ud68d\ub4dd\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$1$\ubc88\uc9f8 \uce90\ub9ad\ud130\ub85c $15$\ubd84\uc5d0 \uac78\uccd0 $1$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \uc7a1\uc544 $10$\uba54\uc18c \ud68d\ub4dd<\/li>\r\n\t<li>$2$\ubc88\uc9f8 \uce90\ub9ad\ud130\ub85c $15$\ubd84\uc5d0&nbsp;\uac78\uccd0 $2$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \uc7a1\uc544 $100$\uba54\uc18c \ud68d\ub4dd<\/li>\r\n<\/ul>\r\n\r\n<p>$1$\ubc88\uc9f8 \uce90\ub9ad\ud130\uac00 $14$\ubd84 $59$\ucd08 \ub3d9\uc548&nbsp;\ub123\uc744 \uc218 \uc788\ub294 \ub370\ubbf8\uc9c0\ub294 $8\\,990$\uc774\ub2e4. \ub0a8\uc740 \uc2dc\uac04 $1$\ucd08 \ub3d9\uc548 $1$\ubc88\uc9f8 \ubcf4\uc2a4\uc640 $3$\ubc88\uc9f8 \ubcf4\uc2a4\ub97c \ubaa8\ub450 \uc7a1\uc744 \uc218 \uc5c6\uc5b4, \uc704\uc640 \uac19\uc740 \uacb0\uacfc\uac00 \ub098\uc624\uac8c \ub41c\ub2e4.<\/p>\r\n"},{"problem_id":"29792","problem_lang":"1","title":"Boss Raid Routine","description":"<p>Kao has been playing <em>MapleStory<\/em> for a while and has developed $N$ characters.<\/p>\r\n\r\n<p>Feeling the need to earn mesos for ongoing upgrades consistently, Kao decides to use the characters he&nbsp;developed to earn mesos. To defeat bosses efficiently, he decides to use each character for a maximum of $15$ minutes a day and to use at most $M$ characters to defeat bosses.<\/p>\r\n\r\n<p>When a character inflicts damage on a boss, the boss&#39;s HP decreases by that amount. If the boss&#39;s HP reaches $0$ or below, the boss is defeated. Damage is calculated every second; thus, damage applied in less than one second is not counted.<\/p>\r\n\r\n<p>Each character can deal a fixed amount of damage every second for $15$ minutes. Time spent moving to other bosses after defeating one is not counted. Each character can defeat each boss only once, but if another character has defeated a boss, the current character can defeat it if they haven&#39;t already. It&#39;s not possible to switch characters while fighting a boss, and the boss&#39;s HP is not shared among characters, meaning a single character must defeat each boss from the start to the end.<\/p>\r\n\r\n<p>Given the HP and meso reward of the boss monsters and the damage information of the characters, find the maximum amount of meso that Kao can earn in a day according to his plan.<\/p>\r\n","input":"<p>The first line contains the number of characters $N$, the number of characters to be used in a day $M$, and the number of different bosses $K$, separated by spaces.&nbsp;$(1 \\le M \\le N \\le 49;$ $1 \\le K \\le 13)$<\/p>\r\n\r\n<p>The following $N$ lines provide the damage $D$ that each character can deal in one second.&nbsp;$(1 \\le&nbsp;D \\le 10^{11})$<\/p>\r\n\r\n<p>The following $K$ lines give the HP $P$ of the boss, and the meso $Q$ rewarded for defeating it, separated by spaces. $(1 \\le&nbsp;P \\le 2.66&nbsp;\\times 10^{11};$ $1 \\le&nbsp;Q \\le&nbsp;1\\,596\\,506)$<\/p>\r\n\r\n<p>All input numbers are given as&nbsp;integers.<\/p>\r\n","output":"<p>Output the maximum amount of meso that Kao can earn in a day by defeating bosses according to his plan.<\/p>\r\n","hint":"<p>The limit for boss HP&nbsp;$P=2.66&nbsp;\\times 10^{11}$ and meso reward $Q=1\\,596\\,506$ are based on the most recent stats&nbsp;as of the August 10, 2023 update. These figures are taken from the boss with the most health (Chaos Horntail) and the highest price for a reward (Normal Papulatus) among the daily bosses.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p>The following plan can earn $110$ mesos.<\/p>\r\n\r\n<ul>\r\n\t<li>Defeat $2^\\text{nd}$ boss for $15$ minutes by the $2^\\text{nd}$ character to earn $40$ mesos<\/li>\r\n\t<li>Defeat $3^\\text{rd}$ boss for $5$ minutes by the $1^\\text{st}$ character to earn $30$ mesos<\/li>\r\n\t<li>Defeat $3^\\text{rd}$ boss for $10$ minutes by the $2^\\text{nd}$ character to earn $40$ mesos<\/li>\r\n<\/ul>\r\n","sample_explain_2":"<p>The following plan can earn $110$ mesos.<\/p>\r\n\r\n<ul>\r\n\t<li>Defeat $1^\\text{st}$ boss for $15$ minutes by the $1^\\text{st}$ character to earn $10$ mesos<\/li>\r\n\t<li>Defeat $2^\\text{nd}$ boss for $15$ minutes by the $2^\\text{nd}$ character to earn $100$ mesos<\/li>\r\n<\/ul>\r\n\r\n<p>The damage the $1^\\text{st}$ character can deal for $14$ minutes and $59$ seconds is $8\\,990$. As subsecond damages are calculated as $0$, they can&#39;t defeat both the $1^\\text{st}$ and the $3^\\text{rd}$ boss in the remaining $1$ second.<\/p>\r\n"}]