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문제

상근이네 자동차 공장에는 직원이 N명 있다. 이 공장은 자동차를 컨베이어 벨트에 올려놓고 차를 만든다. 직원은 1번부터 N번까지 번호가 매겨져 있다. 직원 1은 컨베이어 벨트의 가장 왼쪽에 있고, N은 오른쪽에 있다. 각 직원이 하는 일은 모두 다르다.

차 한 대를 만들려면, 직원 1(상근)이부터 작업을 시작한다. 상근이가 작업을 끝내면 직원 2가 작업을 시작하고, 직원 2가 작업을 끝내면 직원 3이 작업을 시작한다. 그리고 직원 N이 작업을 끝내면 그 때 차가 완성되는 것이다. 차 M대를 만들려면, 1부터 M번까지 순서대로 차를 만들어야 한다.

각 직원 i가 자신의 일을 끝내는데 필요한 시간은 Ti이다. 또, 각 자동차 j의 복잡도는 Fj이다. 직원 i가 자동차 j의 작업을 완료하는데 필요한 시간은 Ti*Fj가 된다.

어떤 직원이 자신의 작업을 끝낸다면, 그 차는 즉시 다음 직원에게 넘겨진다. 따라서, 그 때, 다음 직원이 일을 하고 있으면 안 된다.

모든 일은 상근이가 시작한다. 상근이는 위와 같이 어떤 직원이 작업을 끝내고 다음 직원에게 차를 넘겼는데, 다음 직원이 일을 하고 있는 상황이 발생하지 않게 하려고 한다. 그렇게 하기 위해서 상근이는 작업을 하지 않고 기다려야 하는 시간이 있다. 이때, 이 시간을 최소로 하려고 한다.

모든 직원이 자신의 일을 끝내는데 필요한 시간과 모든 자동차의 복잡도가 주어진다. 이때, 차를 모두 만들기 위해서 필요한 시간을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N과 M이 주어진다. (1 ≤ N, M ≤ 100,000)

다음 N개 줄에는 직원 i의 작업 시간 Ti가 주어진다. (1 ≤ Ti ≤ 10,000)

다음 M개 줄에는 자동차 j의 복잡도 Fj가 주어진다. (1 ≤ Fj ≤ 10,000)

출력

첫째 줄에 자동차를 모두 만들기 위해 필요한 최소 시간을 출력한다.

예제 입력 1

3 3
2
1
1
2
1
1

예제 출력 1

11

4분이 지나면, 직원 1이 첫 번째 차를 만드는 작업을 완료한다. 그리고 즉시 다음 직원에게 차를 넘긴다. 하지만, 바로 두 번째 차를 만드는 직업을 시작하면 안 된다. 그 이유는 7분이 지난 후에, 두 번째 직원은 두 번째 차 작업을 끝냈지만, 세 번째 직원은 아직 첫 번째 차 작업을 끝내지 않았기 때문이다. 따라서, 상근이는 1분을 쉬고 5분이 지났을 때, 두 번째 차를 만들기 시작한다. 또, 세 번째 차는 7분이 지났을 때 시작한다. 첫 번째 차는 작업을 시작한지 8분이 지났을 때 완성되고, 두 번째 차는 9분, 세 번째 차는 11분이 지난 뒤에 완성된다. 따라서, 정답은 11이다.

예제 입력 2

3 3
2
3
3
2
1
2

예제 출력 2

29

예제 입력 3

4 5
3
2
2
2
3
1
2
1
2

예제 출력 3

55
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(1 &le; N, M &le; 100,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uc9c1\uc6d0 i\uc758 \uc791\uc5c5 \uc2dc\uac04 T<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1&nbsp;&le; T<sub>i<\/sub> &le; 10,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uc790\ub3d9\ucc28 j\uc758 \ubcf5\uc7a1\ub3c4 F<sub>j<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(1 &le; F<sub>j<\/sub> &le; 10,000)<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc790\ub3d9\ucc28\ub97c \ubaa8\ub450 \ub9cc\ub4e4\uae30 \uc704\ud574 \ud544\uc694\ud55c \ucd5c\uc18c \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>4\ubd84\uc774 \uc9c0\ub098\uba74, \uc9c1\uc6d0 1\uc774 \uccab \ubc88\uc9f8 \ucc28\ub97c \ub9cc\ub4dc\ub294 \uc791\uc5c5\uc744 \uc644\ub8cc\ud55c\ub2e4. \uadf8\ub9ac\uace0 \uc989\uc2dc \ub2e4\uc74c \uc9c1\uc6d0\uc5d0\uac8c \ucc28\ub97c \ub118\uae34\ub2e4. \ud558\uc9c0\ub9cc, \ubc14\ub85c \ub450 \ubc88\uc9f8 \ucc28\ub97c \ub9cc\ub4dc\ub294 \uc9c1\uc5c5\uc744 \uc2dc\uc791\ud558\uba74 \uc548 \ub41c\ub2e4. \uadf8 \uc774\uc720\ub294 7\ubd84\uc774 \uc9c0\ub09c \ud6c4\uc5d0, \ub450 \ubc88\uc9f8 \uc9c1\uc6d0\uc740 \ub450 \ubc88\uc9f8 \ucc28 \uc791\uc5c5\uc744 \ub05d\ub0c8\uc9c0\ub9cc, \uc138 \ubc88\uc9f8 \uc9c1\uc6d0\uc740 \uc544\uc9c1 \uccab \ubc88\uc9f8 \ucc28 \uc791\uc5c5\uc744 \ub05d\ub0b4\uc9c0 \uc54a\uc558\uae30 \ub54c\ubb38\uc774\ub2e4. \ub530\ub77c\uc11c, \uc0c1\uadfc\uc774\ub294 1\ubd84\uc744 \uc26c\uace0 5\ubd84\uc774 \uc9c0\ub0ac\uc744 \ub54c, \ub450 \ubc88\uc9f8 \ucc28\ub97c \ub9cc\ub4e4\uae30 \uc2dc\uc791\ud55c\ub2e4. \ub610, \uc138 \ubc88\uc9f8 \ucc28\ub294 7\ubd84\uc774 \uc9c0\ub0ac\uc744 \ub54c \uc2dc\uc791\ud55c\ub2e4. \uccab \ubc88\uc9f8 \ucc28\ub294 \uc791\uc5c5\uc744 \uc2dc\uc791\ud55c\uc9c0 8\ubd84\uc774 \uc9c0\ub0ac\uc744 \ub54c \uc644\uc131\ub418\uace0, \ub450 \ubc88\uc9f8 \ucc28\ub294 9\ubd84, \uc138 \ubc88\uc9f8 \ucc28\ub294 11\ubd84\uc774 \uc9c0\ub09c \ub4a4\uc5d0 \uc644\uc131\ub41c\ub2e4. \ub530\ub77c\uc11c, \uc815\ub2f5\uc740 11\uc774\ub2e4.<\/p>\r\n"},{"problem_id":"2821","problem_lang":"1","title":"TRAKA","description":"<p>As mentioned before, there are N workers in Mirko&rsquo;s factory. They are manufacturing cars on a conveyor belt, in a pipeline fashion. Workers are denoted by numbers 1 &ndash; leftmost, to N - rightmost. Each of the workers does his specific job and requires certain amount of time to complete it.&nbsp;<\/p>\r\n\r\n<p>Production of a single car starts with worker #1 (Mirko). After he had finished with his part of the job, worker #2 takes over, after him #3... When worker #N finishes with his part, the car is finished. Mirko and his workers have to produce M cars and they must produce them in order 1 to M.&nbsp;<\/p>\r\n\r\n<p>For every worker i we know T<sub>i<\/sub> - time required for him to do his part of the job. For every car j we know factor of assembly complexity F<sub>j<\/sub>. Time in minutes for worker i to finish his part of he job on the car j is computed as a product T<sub>i<\/sub>F<sub>j<\/sub>.&nbsp;<\/p>\r\n\r\n<p>After some worker has finished working on a car, he has to give it to the next worker instantly, without any delay (weird company policy). For that reason, the worker receiving the car has to be free (he must not be working on some other car). In order to fulfill this condition, Mirko has to choose a good timing to start building a new car. To be efficient, he&rsquo;ll wait minimum number of minutes until he is certain that all of the conditions described are met.&nbsp;<\/p>\r\n\r\n<p>Write a program which will, given worker times and factors of complexity for each car, compute total time required for producing all of the cars.<\/p>\r\n","input":"<p>First line of input contains space-separated positive integers N (1 &le; N &le; 100 000), number of workers, and M (1 &le; M &le; 100 000), number of cars.&nbsp;<\/p>\r\n\r\n<p>i-th of the following N lines contains worker time T<sub>i<\/sub> for the worker i.&nbsp;<\/p>\r\n\r\n<p>j-th of the following M lines contains factor of complexity F<sub>j<\/sub> for the car j.&nbsp;<\/p>\r\n\r\n<p>These conditions hold: 1 &le; T<sub>i<\/sub> &le; 10 000, 1 &le; F<sub>j<\/sub> &le; 10 000.&nbsp;<\/p>\r\n","output":"<p>First and only line of output has to contain required number of minutes.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p>After four minutes, first worker finishes working on the first car. He might start working on the second car immediately, but that would violate a condition that cars have to be passed to next workers as soon as they&rsquo;re done (after seven minutes second worker would finish working on his part of second car, but the third worker would not be free to take over as he would still be working on the first car). That is the reason production of the second car is started after five minutes. Production of the third car starts after seven minutes. First car is finished after eight, second after nine and third after eleven seconds. Total time is then 11.&nbsp;<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p>After four minutes, first worker finishes working on the first car. He might start working on the second car immediately, but that would violate a condition that cars have to be passed to next workers as soon as they&rsquo;re done (after seven minutes second worker would finish working on his part of second car, but the third worker would not be free to take over as he would still be working on the first car). That is the reason production of the second car is started after five minutes. Production of the third car starts after seven minutes. First car is finished after eight, second after nine and third after eleven seconds. Total time is then 11.<\/p>\r\n"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2011/2012 > Contest #3 6번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: jh05013