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문제

그렘린은 작고, 재미있고, 털이 보송보송한 상상 속의 요정이다. 그렘린의 종류는 N가지이며, 편의상 종류별로 1번 부터 N번까지 차례대로 번호가 매겨져있다.

T년 전 한 연구소에서 폭발이 일어나 N 종류의 그렘린이 한 마리씩 생겨났다. 그렘린은 두 단계의 성장 과정(알 → 성장기)을 지나 완전히 자란다.

종류가 i인 그렘린은 알에서 부화하고 Yi년 동안 성장기를 지난다. 성장을 완전히 마친 그렘린은 완전한 성장 직후 Ki개의 알을 낳는다. 각 알 별로 태어나는 그렘린 종류가 다를 수 있고, 알이 부화하는데 걸리는 시간도 다를 수 있다. 안타깝게도 그렘린은 알을 다 낳고 죽는다.

폭발이 일어나고 T년이 지난 현재, 과학자들은 여태까지 존재했던 그렘린 중에 조상이 가장 많은 그렘린이 궁금해졌다. 다만 과학자들은 아직 부화하지 않은 그렘린은 고려하지 않는다. 여기서 조상이란, 부모, 부모의 부모, 부모의 부모의 부모, ... 만 고려한다. 올해 부화 예정인 알들은 모두 부화되었다고 봐도 무방하다.

과학자들을 도와 가장 조상이 많은 그렘린의 조상수를 구하는 프로그램을 작성하시오.

입력

첫 줄에 그렘린 종류의 수 N과 폭발이 일어난 뒤 지난 년 수 T가 주어진다. (1 ≤ N ≤ 100, 1 ≤ T ≤ 1015)

다음 3N개의 줄에 그렘린 종류에 대한 입력이 주어진다.

  • 첫 줄에는 자연수 Ki와 Yi가 주어진다. (1 ≤ Ki ≤ 1000, 1 ≤ Yi ≤ 1000) Ki는 부화하는 알의 개수이고, Yi는 i번 종류의 그렘린이 부화한 뒤 성장기를 거치는 기간을 의미한다.
  • 둘째 줄에는 각 알이 부화되고 나오는 그렘린의 종류를 나타내는 Ki개의 자연수가 주어진다.
  • 셋째 줄에는 각 알이 부화하는데 걸리는 년 수가 주어진다. 이는 1이상 1000 이하의 값이다.

출력

첫 줄에 가장 조상이 많은 그렘린의 조상의 수를 출력한다.

예제 입력 1

2 42
1 10
1
5
1 5
1
5

예제 출력 1

3

힌트

2번 종류 그렘린이 폭발이 일어난 뒤 5년째에 알을 낳고 죽는다.

그 알은 10년째에 부화되어 1번 종류 그렘린이 나온다. 이 그렘린은 20년째에 알을 낳고 죽는다.

그 알은 25년째에 부화되어 1번 종류 그렘린이 나온다. 이 그렘린은 35년째에 알을 낳고 죽는다.

그 알은 40년째에 부화되어 1번 종로 그렘린이 나온다. 이 그렘린의 조상의 수는 3이다.

[{"problem_id":"2895","problem_lang":"0","title":"\uadf8\ub818\ub9b0","description":"<p>\uadf8\ub818\ub9b0\uc740 \uc791\uace0, \uc7ac\ubbf8\uc788\uace0, \ud138\uc774 \ubcf4\uc1a1\ubcf4\uc1a1\ud55c \uc0c1\uc0c1 \uc18d\uc758 \uc694\uc815\uc774\ub2e4. \uadf8\ub818\ub9b0\uc758 \uc885\ub958\ub294 N\uac00\uc9c0\uc774\uba70, \ud3b8\uc758\uc0c1&nbsp;\uc885\ub958\ubcc4\ub85c 1\ubc88 \ubd80\ud130 N\ubc88\uae4c\uc9c0 \ucc28\ub840\ub300\ub85c \ubc88\ud638\uac00 \ub9e4\uaca8\uc838\uc788\ub2e4.<\/p>\r\n\r\n<p>T\ub144 \uc804 \ud55c \uc5f0\uad6c\uc18c\uc5d0\uc11c \ud3ed\ubc1c\uc774 \uc77c\uc5b4\ub098 N \uc885\ub958\uc758 \uadf8\ub818\ub9b0\uc774 \ud55c \ub9c8\ub9ac\uc529 \uc0dd\uaca8\ub0ac\ub2e4. \uadf8\ub818\ub9b0\uc740 \ub450 \ub2e8\uacc4\uc758 \uc131\uc7a5 \uacfc\uc815(\uc54c&nbsp;&rarr; \uc131\uc7a5\uae30)\uc744 \uc9c0\ub098 \uc644\uc804\ud788 \uc790\ub780\ub2e4.<\/p>\r\n\r\n<p>\uc885\ub958\uac00 i\uc778 \uadf8\ub818\ub9b0\uc740 \uc54c\uc5d0\uc11c \ubd80\ud654\ud558\uace0 Yi\ub144 \ub3d9\uc548 \uc131\uc7a5\uae30\ub97c \uc9c0\ub09c\ub2e4. \uc131\uc7a5\uc744 \uc644\uc804\ud788 \ub9c8\uce5c \uadf8\ub818\ub9b0\uc740 \uc644\uc804\ud55c \uc131\uc7a5 \uc9c1\ud6c4 Ki\uac1c\uc758 \uc54c\uc744 \ub0b3\ub294\ub2e4. \uac01 \uc54c \ubcc4\ub85c \ud0dc\uc5b4\ub098\ub294 \uadf8\ub818\ub9b0 \uc885\ub958\uac00 \ub2e4\ub97c \uc218 \uc788\uace0, \uc54c\uc774 \ubd80\ud654\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\ub3c4 \ub2e4\ub97c \uc218 \uc788\ub2e4. \uc548\ud0c0\uae5d\uac8c\ub3c4 \uadf8\ub818\ub9b0\uc740 \uc54c\uc744 \ub2e4 \ub0b3\uace0 \uc8fd\ub294\ub2e4.<\/p>\r\n\r\n<p>\ud3ed\ubc1c\uc774 \uc77c\uc5b4\ub098\uace0&nbsp;T\ub144\uc774 \uc9c0\ub09c \ud604\uc7ac, \uacfc\ud559\uc790\ub4e4\uc740 \uc5ec\ud0dc\uae4c\uc9c0 \uc874\uc7ac\ud588\ub358&nbsp;\uadf8\ub818\ub9b0 \uc911\uc5d0 \uc870\uc0c1\uc774 \uac00\uc7a5 \ub9ce\uc740&nbsp;\uadf8\ub818\ub9b0\uc774 \uad81\uae08\ud574\uc84c\ub2e4. \ub2e4\ub9cc \uacfc\ud559\uc790\ub4e4\uc740 \uc544\uc9c1 \ubd80\ud654\ud558\uc9c0 \uc54a\uc740 \uadf8\ub818\ub9b0\uc740 \uace0\ub824\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc5ec\uae30\uc11c \uc870\uc0c1\uc774\ub780, \ubd80\ubaa8, \ubd80\ubaa8\uc758 \ubd80\ubaa8, \ubd80\ubaa8\uc758 \ubd80\ubaa8\uc758 \ubd80\ubaa8, ... \ub9cc \uace0\ub824\ud55c\ub2e4. \uc62c\ud574 \ubd80\ud654 \uc608\uc815\uc778 \uc54c\ub4e4\uc740 \ubaa8\ub450 \ubd80\ud654\ub418\uc5c8\ub2e4\uace0 \ubd10\ub3c4 \ubb34\ubc29\ud558\ub2e4.<\/p>\r\n\r\n<p>\uacfc\ud559\uc790\ub4e4\uc744 \ub3c4\uc640 \uac00\uc7a5 \uc870\uc0c1\uc774 \ub9ce\uc740 \uadf8\ub818\ub9b0\uc758 \uc870\uc0c1\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uadf8\ub818\ub9b0 \uc885\ub958\uc758 \uc218 N\uacfc \ud3ed\ubc1c\uc774 \uc77c\uc5b4\ub09c \ub4a4 \uc9c0\ub09c \ub144 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 100, 1 &le; T &le; 10<sup>15<\/sup>)<\/p>\r\n\r\n<p>\ub2e4\uc74c 3N\uac1c\uc758 \uc904\uc5d0 \uadf8\ub818\ub9b0 \uc885\ub958\uc5d0 \ub300\ud55c \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab \uc904\uc5d0\ub294 \uc790\uc5f0\uc218 K<sub>i<\/sub>\uc640 Y<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(1 &le; K<sub>i<\/sub> &le; 1000, 1 &le; Y<sub>i<\/sub> &le; 1000) K<sub>i<\/sub>\ub294 \ubd80\ud654\ud558\ub294 \uc54c\uc758 \uac1c\uc218\uc774\uace0, Y<sub>i<\/sub>\ub294 i\ubc88 \uc885\ub958\uc758 \uadf8\ub818\ub9b0\uc774 \ubd80\ud654\ud55c \ub4a4 \uc131\uc7a5\uae30\ub97c \uac70\uce58\ub294 \uae30\uac04\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/li>\r\n\t<li>\ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \uc54c\uc774 \ubd80\ud654\ub418\uace0 \ub098\uc624\ub294 \uadf8\ub818\ub9b0\uc758 \uc885\ub958\ub97c \ub098\ud0c0\ub0b4\ub294&nbsp;Ki\uac1c\uc758 \uc790\uc5f0\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\r\n\t<li>\uc14b\uc9f8 \uc904\uc5d0\ub294 \uac01 \uc54c\uc774 \ubd80\ud654\ud558\ub294\ub370 \uac78\ub9ac\ub294 \ub144 \uc218\uac00&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 1\uc774\uc0c1 1000 \uc774\ud558\uc758 \uac12\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n","output":"<p>\uccab \uc904\uc5d0 \uac00\uc7a5 \uc870\uc0c1\uc774 \ub9ce\uc740 \uadf8\ub818\ub9b0\uc758 \uc870\uc0c1\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>2\ubc88 \uc885\ub958 \uadf8\ub818\ub9b0\uc774 \ud3ed\ubc1c\uc774 \uc77c\uc5b4\ub09c \ub4a4 5\ub144\uc9f8\uc5d0 \uc54c\uc744 \ub0b3\uace0 \uc8fd\ub294\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \uc54c\uc740 10\ub144\uc9f8\uc5d0 \ubd80\ud654\ub418\uc5b4 1\ubc88 \uc885\ub958 \uadf8\ub818\ub9b0\uc774 \ub098\uc628\ub2e4. \uc774 \uadf8\ub818\ub9b0\uc740 20\ub144\uc9f8\uc5d0 \uc54c\uc744 \ub0b3\uace0 \uc8fd\ub294\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \uc54c\uc740 25\ub144\uc9f8\uc5d0 \ubd80\ud654\ub418\uc5b4 1\ubc88 \uc885\ub958 \uadf8\ub818\ub9b0\uc774 \ub098\uc628\ub2e4. \uc774 \uadf8\ub818\ub9b0\uc740 35\ub144\uc9f8\uc5d0 \uc54c\uc744 \ub0b3\uace0 \uc8fd\ub294\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \uc54c\uc740 40\ub144\uc9f8\uc5d0 \ubd80\ud654\ub418\uc5b4 1\ubc88 \uc885\ub85c \uadf8\ub818\ub9b0\uc774 \ub098\uc628\ub2e4. \uc774 \uadf8\ub818\ub9b0\uc758 \uc870\uc0c1\uc758 \uc218\ub294 3\uc774\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2895","problem_lang":"1","title":"GREMLINI","description":"<p>Gremlins are small, funny, fuzzy creatures. In times long gone they used to cause quite a ruckus, but now most of them live decent, honest family lives.<\/p>\r\n\r\n<p>There are N different types of gremlins, coded with numbers 1 to N for your convenience. Legend has it that T years ago a laboratory accident occurred causing N gremlins, one of each type to be born.<\/p>\r\n\r\n<p>As you all know, in order for gremlins to reproduce, no mating rituals are required. Just add a dash of watter and you instantly get a few new cocoons.<\/p>\r\n\r\n<p>Gremlins of type i need exactly Yi years to mature and spawn Ki cocoons. For each cocoon you know how much years does it take to hatch, and which gremlin type is contained within. The original gremlin unfortunately dies while producing cocoons.<\/p>\r\n\r\n<p>Now, T years after the original accident. Scientist wonder what is the longest ancestral chain whose genome is currently represented. They are only interested in ancestors of hatched gremlins, not those still cocooned. You are safe to assume that all gremlins that were supposed to hatch this year did so.<\/p>\r\n","input":"<p>The first line of input contains two integers N and T (1 &le; N &le; 100, 1 &le; T &le; 10<sup>15<\/sup>), number of gremlin types and number of years after the original accident.<\/p>\r\n\r\n<p>Next 3\u2219N lines contain gremlin type descriptions, three lines per type:<\/p>\r\n\r\n<ul>\r\n\t<li>First line contains integers K<sub>i<\/sub> and Y<sub>i<\/sub> (1 &le; K<sub>i<\/sub> &le; 1000, 1 &le; Y<sub>i<\/sub> &le; 1000), number of cocoons formed when this gremlin type spawns and number of years this gremlin type needs to reach maturity.<\/li>\r\n\t<li>The second line contains K<sub>i<\/sub> integers between 1 and N inclusive, types of gremlins hatched from cocoons formed by this gremlin type.<\/li>\r\n\t<li>The third line contains K<sub>i<\/sub> integers between 1 and 1000, representing hatching time for each cocoon, in years.&nbsp;<\/li>\r\n<\/ul>\r\n","output":"<p>The first and only line of output should contain the length of the currently longest ancestral chain.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p>The original gremlin hatched in the accident after 10 years spawns a single cocoon and dies.<\/p>\r\n\r\n<p>15 years after the accident, a new gremlin hatches from the cocoon. His ancestral chain contains one gremlin. 25 years after the accident this gremlin spawns a new cocoon and dies.<\/p>\r\n\r\n<p>30 years after the accident, a new gremlin hatches from the cocoon. His ancestral chain contains two gremlins. 40 years after the accident this gremlin spawns a new cocoon and dies.<\/p>\r\n\r\n<p>42 years after the accident, the current cocoon is not yet hatched, so the longest ancestral chain ever recorded is two gremlins in length.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2009/2010 > Contest #6 6번