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문제

상근이는 양을 복제하려고 한다. 따라서 복제 기계 N개를 구매했다.

복제 기계에는 키보드가 하나씩 달려있고, 양의 정수를 입력할 수 있다. 기계 안에 양이 K마리 있고, 키보드로 p를 입력했다고 하자. 이 상태에서 복제 버튼을 누르면 기계 안에 있는 양은 총 p*K마리가 된다.

기계에 입력하는 p는 항상 소수이어야 한다. 또, 복제 기계에는 최대 용량이 정해져있고, 이 수만큼 양이 들어있을 수 있다.

상근이는 복제를 하기 위해서 기계로 이동하고 버튼을 누르는 것이 매우 귀찮았다. 결국 상근이는 조수 N명을 고용했고, 각 기계 앞에 한 명씩 배정했다. 그 다음, 각 조수에게 다음과 같은 명령을 외칠 것이다.

  • ENTER p - 이 명령은 모든 조수에게 기계에 p를 입력하라는 명령이다. p는 항상 소수이다.
  • CLONE a1, a2, ..., ak - 기계 a1, a2, ..., ak의 앞에 서 있는 조수에게 복제 버튼을 누르라는 명령이다. 조수가 혼란에 빠지지 않게 하기 위해, 각 숫자는 모두 서로 다르다. 하지만, 상근이는 집중력이 매우 부족하기 때문에 한 번에 최대 M개의 숫자만 말할 수 있다.

상근이는 각 기계에 양을 한 마리씩 넣어 놓았다. 기계를 최대한 효율적으로 이용하기 위해서 각 기계의 최대 용량만큼 양을 복제하려고 한다. 양은 복제를 하는 중간에 뺄 수 없다. 또, 목이 아프기 때문에 명령을 최대한 조금 외치려고 한다.

각 기계의 최대 용량과 M이 주어졌을 때, 양을 최대한 많이 만들기 위해서 필요한 명령의 순서를 구하는 프로그램을 작성하시오. 명령의 수는 최소이어야 하며, 가능한 명령의 순서가 여러 가지인 경우에는 아무거나 출려가면 된다.

입력

첫째 줄에 복제 기계의 수 N이 주어진다. (1 ≤ N ≤ 50)

둘째 줄에는 각 기계의 최대 용량이 주어진다. 이 값은 1,000,000,000보다 작은 자연수이다.

셋째 줄에는 상근이가 한 번의 CLONE 명령에서 외칠 수 있는 최대 수의 개수 M이 주어진다. (1 ≤ M ≤ N)

출력

한 줄에 하나씩 상근이가 외치는 명령을 출력한다.

예제 입력 1

3
2 3 6
2

예제 출력 1

ENTER 2
CLONE 1 3
ENTER 3
CLONE 2 3

예제 입력 2

5
25 25 30 25 25
3

예제 출력 2

ENTER 2
CLONE 3
ENTER 5
CLONE 1 2 3
CLONE 5 4 1
CLONE 2 4 5
ENTER 3
CLONE 3
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(1 &le; N &le; 50)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \uae30\uacc4\uc758 \ucd5c\ub300 \uc6a9\ub7c9\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uac12\uc740 1,000,000,000\ubcf4\ub2e4 \uc791\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0\ub294 \uc0c1\uadfc\uc774\uac00 \ud55c \ubc88\uc758 CLONE \uba85\ub839\uc5d0\uc11c \uc678\uce60 \uc218 \uc788\ub294 \ucd5c\ub300 \uc218\uc758 \uac1c\uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; M &le; N)<\/p>\r\n","output":"<p>\ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc0c1\uadfc\uc774\uac00 \uc678\uce58\ub294 \uba85\ub839\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3113","problem_lang":"1","title":"KLONOVI","description":"<p>Simona breeds sheep. Not being patient enough to wait for sheep to multiply naturally, she built a cloning facility with N machines in it.&nbsp;<\/p>\r\n\r\n<p>Cloning machines have keyboards that can be used to type in positive integers. If there are K sheep in a machine and the number p is typed in, after pressing the button &quot;Clone&quot; cloning starts and soon after p&middot;K sheep can be found in the machine! For reasons unknown to Simona, cloning only works if the number p is prime. Also, every machine has a maximum capacity &ndash; the largest number of sheep that it can hold.&nbsp;<\/p>\r\n\r\n<p>Simona got tired of walking from machine to machine pressing buttons. So she hired N assistants, one for each machine, and now yells out commands to the assistants:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>ENTER p &ndash; every assistant types p into the keyboard; p must be prime.&nbsp;<\/li>\r\n\t<li>CLONE a<sub>1<\/sub> a<sub>2<\/sub> ... a<sub>K<\/sub> &ndash; assistants near machines a<sub>1<\/sub>, a<sub>2<\/sub>, ..., a<sub>K<\/sub> all press &quot;Clone&quot;. These numbers are distinct (so that assistants don&#39;t get confused). Because Simona&#39;s concentration is limited, she can say at most M numbers in a single CLONE commands.&nbsp;<\/li>\r\n<\/ul>\r\n\r\n<p>Simona initially puts one sheep into every machine. In order to fully use the machines, Simona wants to fill every machine up to its maximum capacity. Once a sequence of commands begins, it is not allowed to take sheep out of machines. Also, Simona wants to yell out as few commands as possible to fill all machines with sheep.&nbsp;<\/p>\r\n\r\n<p>Write a program that determines any shortest sequence of commands that will completely fill all machines with sheep.&nbsp;<\/p>\r\n","input":"<p>The first line contains the integer N (1 &le; N &le; 50), the number of cloning machines.&nbsp;<\/p>\r\n\r\n<p>The second line contains N integers, each less than 1 000 000 000. These numbers are the capacities of the machines.&nbsp;<\/p>\r\n\r\n<p>The third line contains the integer M (1 &le; M &le; N), the largest number of machines Simona can trigger in a single CLONE command.&nbsp;<\/p>\r\n","output":"<p>Output Simona&#39;s commands, each on its own line. If multiple solutions exist, output any of them.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]