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문제

재현이는 초고층 건물인 "제2사과타워"를 짓기 위해 노동자들을 고용하고 있다. 1번부터 N번까지 총 N명의 노동자들이 지원했는데, i (1 ≤ i ≤ N)번째 노동자는 최저임금 Si를 가지고 있어 Si보다 크거나 같은 만큼의 임금을 받아야 하며, 또한 Qi라는 건설 자격증 레벨을 가지고 있다.

최근 정부에서는 건설 자격증을 활성화하기 위해서, 노동자들의 임금을 항상 자격증 레벨에 비례하기 지급하게 하는 규정을 만들었다. 만약 A라는 노동자의 자격증 레벨이 Qa이고, B라는 노동자의 자격증 레벨이 Qb라면, A의 임금은 Qa * k, B의 임금은 Qb * k가 되어야 한다. 노동자들에게 지급하는 임금은 정수가 아닌 실수 범위여도 무방하다.

재현이는 수중에 W달러를 가지고 있으며, 사실 재현이는 자격증에 대해서는 별로 관심이 없고 그저 건물을 빨리 짓고 싶기 때문에, 자격증 레벨과 상관없이 현재 자금 내에서 가장 많은 노동자들을 고용하고 싶어 한다. 만약 고용할 수 있는 노동자의 수가 같다면, 노동자들에게 최소 비용을 지급하는 고용 방안을 원하며, 노동자의 수와 비용이 같다면 어떤 방법이든지 상관 없다. 재현이를 도와, 고용할 수 있는 노동자의 최대 수와 그 때 고용해야 할 노동자를 구하여라.

입력

표준 입력으로부터 다음의 데이터를 읽어야 한다:

  • 첫째 줄에는 N과 W가 주어진다.
  • 이후 N개 줄에 각 노동자의 정보가 주어진다. 이후 주어지는 정보의 i번째 줄에는 i번째 노동자의 최저임금 Si, 자격증 레벨 Qi가 주어진다.

출력

표준 출력에 최대로 고용할 수 있는 노동자의 수 H를 출력하며, 이후 H개의 줄에 고용하고 싶어하는 노동자들의 번호를 출력한다. 노동자들의 번호는 제각기 달라야 하며 순서는 어떤 순서여도 상관없다.

제한

  • 1 ≤ N ≤ 500,000 지원 노동자의 수
  • 1 ≤ Si ≤ 20,000 노동자 i의 최저임금
  • 1 ≤ Qi ≤ 20,000 노동자 i의 자격증 레벨
  • 1 ≤ W ≤ 10,000,000,000 사용할 수 있는 돈의 양
  • 입력으로 주어지는 수는 모두 정수이다.

예제 입력 1

4 100
5 1000
10 100
8 10
20 1

예제 출력 1

2
2
3

예제 입력 2

3 4
1 2
1 3
1 3

예제 출력 2

3
1
2
3

예제 입력 3

3 40
10 1
10 2
10 3

예제 출력 3

2
2
3
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There are N candidates applying for the job, numbered from 1 to N inclusive. Each candidate k requires that if he is hired, he must be paid at least Sk dollars. Also, each candidate k has a qualification level Qk. The regulations of the construction industry require that you pay your workers in proportion to their qualification level, relative to each other. For example, if you hire two workers A and B, and QA = 3 * QB, then you have to pay worker A exactly three times as much as you pay worker B. You are allowed to pay your workers non-integer amounts of money. This even includes quantities that cannot be written with a finite number of digits in decimal form, such as a third or a sixth of a dollar.<\/p>\r\n\r\n<p>You have W dollars at hand and you want to hire as many workers as possible. You decide whom to hire and how much to pay them, but you have to meet the minimum salary requirements of those you choose to hire, and you have to obey the industry regulations. 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You must hire as many of them as possible and you must do so with as little money as possible, while complying with the industry regulations specified above.&nbsp;<\/p>\r\n\r\n<p>The maximum value of W does not fit in 32 bits. You have to use a 64-bit data type, such as long long in C\/C++ or int64 in Pascal, in order to store the value of W in a single variable. Please see the technical info sheet for details.<\/p>\r\n","input":"<p>Your program must read from standard input the following data:<\/p>\r\n\r\n<ul>\r\n\t<li>The first line contains the integers N and W, separated by a space.<\/li>\r\n\t<li>The next N lines describe the candidates, one candidate per line. The kth of these lines describes candidate number k and it contains the integers Sk and Qk, separated by a space.<\/li>\r\n<\/ul>\r\n\r\n<ul>\r\n\t<li>1 &le; N &le; 500,000 The number of candidates<\/li>\r\n\t<li>1 &le; Sk &le; 20,000 The minimum salary requirement of candidate k<\/li>\r\n\t<li>1 &le; Qk &le; 20,000 The qualification level of candidate k<\/li>\r\n\t<li>1 &le; W &le; 10,000,000,000 The amount of money available to you&nbsp;<\/li>\r\n<\/ul>\r\n","output":"<p>Your program must write to standard output the following data:<\/p>\r\n\r\n<ul>\r\n\t<li>The first line must contain a single integer H, the number of workers that you hire.<\/li>\r\n\t<li>The next H lines must list the identifying numbers of the candidates you choose to hire (each of them a different number between 1 and N), one per line, in any order.<\/li>\r\n<\/ul>\r\n","hint":"<p>Sample 1<\/p>\r\n\r\n<p>The only combination for which you can afford to hire two workers and still meet all the constraints is if you select workers 2 and 3. You can pay them 80 and 8 dollars respectively and thus fit in your budget of 100.&nbsp;<\/p>\r\n\r\n<p>Sample 2<\/p>\r\n\r\n<p>Here you can afford to hire all three workers. You pay 1 dollar to worker 1 and 1.50 dollars each to workers 2 and 3, and you manage to hire everyone with the 4 dollars that you have.&nbsp;<\/p>\r\n\r\n<p>Sample 3<\/p>\r\n\r\n<p>Here you cannot afford to hire all three workers, as it would cost you 60 dollars, but you can afford to hire any two of them. You choose to hire workers 2 and 3 because they would cost you the smallest sum of money, compared to the other two-worker combinations. You can pay 10 dollars to worker 2 and 15 dollars to worker 3 for a total of 25 dollars. If you were to hire workers 1 and 2 you would have to pay them at least 10 and 20 dollars respectively. If you were to hire 1 and 3, then you would have to pay them at least 10 and 30 dollars respectively.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > International Olympiad in Informatics > IOI 2009 > Day 1 2번

  • 문제를 번역한 사람: koosaga
  • 문제의 오타를 찾은 사람: rdd6584