시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 128 MB 39 19 19 50.000%

문제

한 범죄 조직에서의 오랜 기간에 걸친 첩보 활동 끝에, 당신은 이제 그 조직을 와해시킬 시도를 해보려 한다. 하지만 당신 혼자서는 이 일을 성공적으로 끝낼 수 없다. 그래서 당신은 조직원 몇 명을 매수해 일을 진행하려 하지만, 당신에게 주어진 예산은 한정되어 있다.

다행히도 당신은 사람을 파악하는 데 천부적인 재능이 있다. 그래서 어떤 조직원이 조직을 배반할 생각이 있다면, 당신은 그에게 어느 정도의 돈을 줘야 할 지를 이미 알고 있다. 게다가, 당신은 그들이 성공적으로 변절하여 완벽히 당신의 편이 될 확률까지도 알고 있다. 특별히 다른 방법이 존재하지 않기에 당신은 이제부터 실제로 조직원들에게 직접 접근하여 매수를 시도하려 한다. 만일 어떤 조직원이 돈을 받고도 매수되지 않았다면 당신은 다시는 그 조직원을 매수하려 시도할 수 없다.

각 조직원들에 대한 정보, 즉 그들이 요구할 돈과 변절할 확률이 주어지고, 당신이 필요한 최소한의 변절자 수가 주어질 때, 과연 이번 계획이 어느 정도의 확률로 성공할 지 계산할 수 있을까?

입력

입력의 첫 줄엔 테스트 케이스의 수가 주어진다. 이 수는 100을 넘지 않는다.

각 테스트 케이스는 다음과 같이 구성된다.

  • 공백으로 구분된 세 개의 정수 n, c, m (1 ≤ n, c ≤ 16 and 1 ≤ m ≤ 1000) : 접선할 수 있는 조직원의 수, 당신이 필요로 하는 최소한의 조직원 수, 예산
  • n줄에 걸쳐 두 개의 정수 b, p (0 ≤ b ≤ 1 000 , 0 ≤ p ≤ 100) : 매수를 시도하는 데 필요한 금액, 그 조직원이 성공적으로 당신의 편이 될 확률( % 값 )

출력

각 테스트 케이스에 대해 다음을 출력한다.

  • 당신이 가장 이상적으로 계획을 진행했을 때, c명의 조직원을 매수하는 데 성공할 확률. 오차는 소수점 7째 자리부터 허용한다.

예제 입력 1

2
4 3 1000
300 40
300 50
300 60
300 70
4 2 1000
100 80
700 50
400 20
500 20

예제 출력 1

0.21
0.408
[{"problem_id":"9368","problem_lang":"0","title":"\ub9e4\uc218","description":"<p>\ud55c \ubc94\uc8c4 \uc870\uc9c1\uc5d0\uc11c\uc758 \uc624\ub79c \uae30\uac04\uc5d0 \uac78\uce5c \ucca9\ubcf4 \ud65c\ub3d9 \ub05d\uc5d0, \ub2f9\uc2e0\uc740 \uc774\uc81c \uadf8 \uc870\uc9c1\uc744 \uc640\ud574\uc2dc\ud0ac \uc2dc\ub3c4\ub97c \ud574\ubcf4\ub824 \ud55c\ub2e4. \ud558\uc9c0\ub9cc \ub2f9\uc2e0 \ud63c\uc790\uc11c\ub294 \uc774 \uc77c\uc744 \uc131\uacf5\uc801\uc73c\ub85c \ub05d\ub0bc \uc218 \uc5c6\ub2e4. \uadf8\ub798\uc11c \ub2f9\uc2e0\uc740 \uc870\uc9c1\uc6d0 \uba87 \uba85\uc744 \ub9e4\uc218\ud574 \uc77c\uc744 \uc9c4\ud589\ud558\ub824 \ud558\uc9c0\ub9cc, \ub2f9\uc2e0\uc5d0\uac8c \uc8fc\uc5b4\uc9c4 \uc608\uc0b0\uc740 \ud55c\uc815\ub418\uc5b4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ud589\ud788\ub3c4 \ub2f9\uc2e0\uc740 \uc0ac\ub78c\uc744 \ud30c\uc545\ud558\ub294 \ub370 \ucc9c\ubd80\uc801\uc778 \uc7ac\ub2a5\uc774 \uc788\ub2e4. \uadf8\ub798\uc11c \uc5b4\ub5a4 \uc870\uc9c1\uc6d0\uc774 \uc870\uc9c1\uc744 \ubc30\ubc18\ud560 \uc0dd\uac01\uc774 \uc788\ub2e4\uba74, \ub2f9\uc2e0\uc740 \uadf8\uc5d0\uac8c \uc5b4\ub290 \uc815\ub3c4\uc758 \ub3c8\uc744 \uc918\uc57c \ud560 \uc9c0\ub97c \uc774\ubbf8 \uc54c\uace0 \uc788\ub2e4. \uac8c\ub2e4\uac00, \ub2f9\uc2e0\uc740 \uadf8\ub4e4\uc774 \uc131\uacf5\uc801\uc73c\ub85c \ubcc0\uc808\ud558\uc5ec \uc644\ubcbd\ud788 \ub2f9\uc2e0\uc758 \ud3b8\uc774 \ub420 \ud655\ub960\uae4c\uc9c0\ub3c4 \uc54c\uace0 \uc788\ub2e4. \ud2b9\ubcc4\ud788 \ub2e4\ub978 \ubc29\ubc95\uc774&nbsp;\uc874\uc7ac\ud558\uc9c0 \uc54a\uae30\uc5d0 \ub2f9\uc2e0\uc740 \uc774\uc81c\ubd80\ud130 \uc2e4\uc81c\ub85c \uc870\uc9c1\uc6d0\ub4e4\uc5d0\uac8c \uc9c1\uc811 \uc811\uadfc\ud558\uc5ec \ub9e4\uc218\ub97c \uc2dc\ub3c4\ud558\ub824 \ud55c\ub2e4. \ub9cc\uc77c \uc5b4\ub5a4 \uc870\uc9c1\uc6d0\uc774 \ub3c8\uc744 \ubc1b\uace0\ub3c4 \ub9e4\uc218\ub418\uc9c0 \uc54a\uc558\ub2e4\uba74 \ub2f9\uc2e0\uc740 \ub2e4\uc2dc\ub294 \uadf8 \uc870\uc9c1\uc6d0\uc744 \ub9e4\uc218\ud558\ub824 \uc2dc\ub3c4\ud560&nbsp;\uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uc870\uc9c1\uc6d0\ub4e4\uc5d0 \ub300\ud55c \uc815\ubcf4, \uc989 \uadf8\ub4e4\uc774 \uc694\uad6c\ud560 \ub3c8\uacfc \ubcc0\uc808\ud560 \ud655\ub960\uc774 \uc8fc\uc5b4\uc9c0\uace0, \ub2f9\uc2e0\uc774 \ud544\uc694\ud55c \ucd5c\uc18c\ud55c\uc758 \ubcc0\uc808\uc790 \uc218\uac00 \uc8fc\uc5b4\uc9c8 \ub54c, \uacfc\uc5f0 \uc774\ubc88 \uacc4\ud68d\uc774 \uc5b4\ub290 \uc815\ub3c4\uc758 \ud655\ub960\ub85c \uc131\uacf5\ud560 \uc9c0 \uacc4\uc0b0\ud560 \uc218 \uc788\uc744\uae4c?<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d4 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc218\ub294 100\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\uc131\ub41c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc138 \uac1c\uc758 \uc815\uc218 n, c, m (1 &le; n, c &le; 16 and 1 &le; m &le; 1000) : \uc811\uc120\ud560 \uc218 \uc788\ub294 \uc870\uc9c1\uc6d0\uc758 \uc218, \ub2f9\uc2e0\uc774 \ud544\uc694\ub85c \ud558\ub294 \ucd5c\uc18c\ud55c\uc758 \uc870\uc9c1\uc6d0 \uc218, \uc608\uc0b0<\/li>\r\n\t<li>n\uc904\uc5d0 \uac78\uccd0 \ub450 \uac1c\uc758 \uc815\uc218 b, p (0 &le; b &le; 1 000 ,&nbsp;0 &le; p &le; 100) : \ub9e4\uc218\ub97c \uc2dc\ub3c4\ud558\ub294 \ub370 \ud544\uc694\ud55c \uae08\uc561, \uadf8 \uc870\uc9c1\uc6d0\uc774 \uc131\uacf5\uc801\uc73c\ub85c \ub2f9\uc2e0\uc758 \ud3b8\uc774 \ub420 \ud655\ub960( % \uac12&nbsp;)<\/li>\r\n<\/ul>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ub2e4\uc74c\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub2f9\uc2e0\uc774 \uac00\uc7a5 \uc774\uc0c1\uc801\uc73c\ub85c \uacc4\ud68d\uc744 \uc9c4\ud589\ud588\uc744 \ub54c,&nbsp;c\uba85\uc758 \uc870\uc9c1\uc6d0\uc744 \ub9e4\uc218\ud558\ub294 \ub370 \uc131\uacf5\ud560 \ud655\ub960. \uc624\ucc28\ub294 \uc18c\uc218\uc810 7\uc9f8 \uc790\ub9ac\ubd80\ud130 \ud5c8\uc6a9\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9368","problem_lang":"1","title":"Bribe","description":"<p>After having done a lot of spying and in\ufb01ltrating a criminal network, you are now ready to try and dismantle it. This, however, requires the cooperation of a certain number of the henchmen. This in turn requires money in order to bribe them, but due to budget cuts, you only have a limited amount of money.<\/p>\r\n\r\n<p>Fortunately, you are an excellent judge of character, so for each of the henchmen you are considering to bribe, you know what amount of money they will ask for. Furthermore, you know the probability that they will then successfully convert, as opposed to taking the money and making a run for it. There is no particular rush, so after each attempted conversion you can establish whether it was successful or not, before you move on to someone else. Of course, if it was not successful, then you cannot try to bribe this henchman a second time.<\/p>\r\n\r\n<p>Given all this information on the henchmen, the amount of money that you have at your disposal, and the number of henchmen you need to convert, can you work out the probability that this operation will be a success?<\/p>\r\n","input":"<p>On the \ufb01rst line one positive number: the number of test cases, at most 100. After that per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with three space-separated integers n, c and m (1 &le; n, c &le; 16 and 1 &le; m &le; 1 000): the number of henchmen that are susceptible to bribe, the number you need to convert, and the amount of money that you have, respectively.<\/li>\r\n\t<li>n lines with two space-separated integers b and p (0 &le; b &le; 1 000 and 0 &le; p &le; 100): the amount of money you need to bribe each henchman, and the probability (as a percentage) that he will be successfully converted, respectively<\/li>\r\n<\/ul>\r\n","output":"<p>Per test case:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with a single \ufb02oating point number: the probability that you will succeed in converting c henchmen, if you take an optimal approach. This number should be accurate up to 10<sup>-6<\/sup> relative or absolute precision.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]