시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

현성이가 자신의 형 현민이와 게임을 한다. 이 게임은 특정한 맵에서 진행된다.

이 게임에서 사용하는 맵은 N개의 원과 M개의 화살표가 그려져 있는데, 각 화살표는 서로 다른 두 원을 연결하고 있다.

게임을 시작하면, 맨 처음에 말은 1번째 원 위에 있다. 매 턴마다 현민이가 1 이상의 정수를 말한다. 그런 후에는 현성이가 현민이가 말한 수만큼 말을 움직인다. 말은 오직 화살표 방향으로만 이동할 수 있다.

현성이가 말을 움직여서 N번째 원 위로 도착하면 현성이가 이긴다. 다만, 현성이가 말을 더 움직여야 하는 상황에서 N번째 원으로 온 경우는 게임이 끝나지 않는다. 만약 현성이가 말을 움직이다가 더 이상 말을 움직일 수 없는 상황이 온 경우 현민이가 이긴다. 또, 게임이 무한히 반복된다면 현민이의 승리로 간주한다.

현민이는 두뇌 서바이벌 프로그램에서 준우승할 정도로 똑똑하기 때문에 게임을 할 때마다 계속 현민이가 이겼다. 그래서 현민이는 현성이의 멘탈을 위해 조금 봐주기로 했다. 현민이는 현성이를 위해 매 턴을 시작할 때 부르는 수를 a, b, c 중에서 고르기로 했다. 그래도 현성이가 현민이를 이기기에는 역부족이었다.

멘탈이 증발한 현성이는 당신에게 현민이를 이기는 전략을 짜달라고 요청하였다. 현성이를 도와 현민이를 이기는 전략이 있는지 구하고 만약 있다면 최소 몇 턴만에 게임을 끝낼 수 있는지 구하여라.

입력

첫 번째 줄에는 N, M, a, b, c가 주어진다. N은 원의 개수, M은 화살표의 개수, a, b, c는 현민이가 부르는 수를 의미한다. (2 ≤ N ≤ 50, 0 ≤ M ≤ N(N-1), 1 ≤ a, b, c ≤ 100)

두 번째 줄부터 M개의 줄에는 각 화살표의 시작점, 끝점 u, v가 주어진다. (1 ≤ u ≠ v ≤ 100) 어떤 두 화살표에 대해서도 시작점과 끝점이 완전히 같지는 않다.

출력

만약 현성이가 현민이를 이길 수 없다면 'IMPOSSIBLE'을 출력한다.

그렇지 않은 경우, 현성이가 현민이를 이기기 위해 필요한 최소 턴의 수를 출력한다.

예제 입력 1

3 3 1 2 4
1 2
2 3
3 1

예제 출력 1

IMPOSSIBLE

예제 입력 2

8 12 1 2 3
1 2
2 3
1 4
2 4
3 4
1 5
5 8
4 6
6 7
4 8
6 8
7 8

예제 출력 2

2

힌트

첫 번째 예제에서는 현민이가 1, 2를 번갈아 부르면 게임이 끝나지 않기 때문에 현민이가 이긴다.

두 번째 예제에서는 아래와 같은 전략을 세우면 된다.

  • 만약 현민이가 2나 3을 부른다면 한 번만에 N번 원으로 갈 수 있다.
  • 만약 현민이가 1을 부른다면 4번 원으로 가는 것이 최적이다. 현성이가 4번 원으로 간다면 현민이가 다음 턴에 무슨 수를 부르던지 한 번에 N번 원으로 갈 수 있다. 만약 현성이가 5번 원으로 간다면 현민이가 2나 3을 부르면 현민이가 이긴다. 현성이가 2번 원으로 간다면 현성이가 이길 수는 있지만 더 많은 턴을 요구한다.

두 번째 예제의 맵
 

[{"problem_id":"11749","problem_lang":"0","title":"\ud615\uc81c \uac8c\uc784","description":"<p>\ud604\uc131\uc774\uac00 \uc790\uc2e0\uc758 \ud615 \ud604\ubbfc\uc774\uc640 \uac8c\uc784\uc744 \ud55c\ub2e4. \uc774 \uac8c\uc784\uc740 \ud2b9\uc815\ud55c \ub9f5\uc5d0\uc11c \uc9c4\ud589\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uac8c\uc784\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \ub9f5\uc740 N\uac1c\uc758 \uc6d0\uacfc M\uac1c\uc758 \ud654\uc0b4\ud45c\uac00 \uadf8\ub824\uc838 \uc788\ub294\ub370, \uac01 \ud654\uc0b4\ud45c\ub294 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc6d0\uc744 \uc5f0\uacb0\ud558\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc744 \uc2dc\uc791\ud558\uba74, \ub9e8 \ucc98\uc74c\uc5d0 \ub9d0\uc740 1\ubc88\uc9f8 \uc6d0 \uc704\uc5d0 \uc788\ub2e4. \ub9e4 \ud134\ub9c8\ub2e4 \ud604\ubbfc\uc774\uac00 1 \uc774\uc0c1\uc758 \uc815\uc218\ub97c \ub9d0\ud55c\ub2e4. \uadf8\ub7f0 \ud6c4\uc5d0\ub294 \ud604\uc131\uc774\uac00 \ud604\ubbfc\uc774\uac00 \ub9d0\ud55c \uc218\ub9cc\ud07c \ub9d0\uc744 \uc6c0\uc9c1\uc778\ub2e4. \ub9d0\uc740 \uc624\uc9c1 \ud654\uc0b4\ud45c \ubc29\ud5a5\uc73c\ub85c\ub9cc \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud604\uc131\uc774\uac00 \ub9d0\uc744 \uc6c0\uc9c1\uc5ec\uc11c N\ubc88\uc9f8 \uc6d0 \uc704\ub85c \ub3c4\ucc29\ud558\uba74 \ud604\uc131\uc774\uac00 \uc774\uae34\ub2e4. \ub2e4\ub9cc, \ud604\uc131\uc774\uac00 \ub9d0\uc744 \ub354 \uc6c0\uc9c1\uc5ec\uc57c \ud558\ub294 \uc0c1\ud669\uc5d0\uc11c N\ubc88\uc9f8 \uc6d0\uc73c\ub85c \uc628 \uacbd\uc6b0\ub294 \uac8c\uc784\uc774 \ub05d\ub098\uc9c0 \uc54a\ub294\ub2e4. \ub9cc\uc57d \ud604\uc131\uc774\uac00 \ub9d0\uc744 \uc6c0\uc9c1\uc774\ub2e4\uac00 \ub354 \uc774\uc0c1 \ub9d0\uc744 \uc6c0\uc9c1\uc77c \uc218 \uc5c6\ub294 \uc0c1\ud669\uc774 \uc628 \uacbd\uc6b0 \ud604\ubbfc\uc774\uac00 \uc774\uae34\ub2e4. \ub610, \uac8c\uc784\uc774 \ubb34\ud55c\ud788 \ubc18\ubcf5\ub41c\ub2e4\uba74 \ud604\ubbfc\uc774\uc758 \uc2b9\ub9ac\ub85c \uac04\uc8fc\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud604\ubbfc\uc774\ub294 \ub450\ub1cc \uc11c\ubc14\uc774\ubc8c \ud504\ub85c\uadf8\ub7a8\uc5d0\uc11c \uc900\uc6b0\uc2b9\ud560 \uc815\ub3c4\ub85c \ub611\ub611\ud558\uae30 \ub54c\ubb38\uc5d0 \uac8c\uc784\uc744 \ud560 \ub54c\ub9c8\ub2e4 \uacc4\uc18d \ud604\ubbfc\uc774\uac00 \uc774\uacbc\ub2e4. \uadf8\ub798\uc11c \ud604\ubbfc\uc774\ub294 \ud604\uc131\uc774\uc758 \uba58\ud0c8\uc744 \uc704\ud574 \uc870\uae08 \ubd10\uc8fc\uae30\ub85c \ud588\ub2e4. \ud604\ubbfc\uc774\ub294 \ud604\uc131\uc774\ub97c \uc704\ud574 \ub9e4 \ud134\uc744 \uc2dc\uc791\ud560 \ub54c \ubd80\ub974\ub294 \uc218\ub97c a, b, c \uc911\uc5d0\uc11c \uace0\ub974\uae30\ub85c \ud588\ub2e4. \uadf8\ub798\ub3c4 \ud604\uc131\uc774\uac00 \ud604\ubbfc\uc774\ub97c \uc774\uae30\uae30\uc5d0\ub294 \uc5ed\ubd80\uc871\uc774\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uba58\ud0c8\uc774 \uc99d\ubc1c\ud55c \ud604\uc131\uc774\ub294 \ub2f9\uc2e0\uc5d0\uac8c \ud604\ubbfc\uc774\ub97c \uc774\uae30\ub294 \uc804\ub7b5\uc744 \uc9dc\ub2ec\ub77c\uace0 \uc694\uccad\ud558\uc600\ub2e4. \ud604\uc131\uc774\ub97c \ub3c4\uc640 \ud604\ubbfc\uc774\ub97c \uc774\uae30\ub294 \uc804\ub7b5\uc774 \uc788\ub294\uc9c0 \uad6c\ud558\uace0 \ub9cc\uc57d \uc788\ub2e4\uba74 \ucd5c\uc18c \uba87 \ud134\ub9cc\uc5d0 \uac8c\uc784\uc744 \ub05d\ub0bc \uc218 \uc788\ub294\uc9c0 \uad6c\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 N, M, a, b, c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. N\uc740 \uc6d0\uc758 \uac1c\uc218, M\uc740 \ud654\uc0b4\ud45c\uc758 \uac1c\uc218, a, b, c\ub294 \ud604\ubbfc\uc774\uac00 \ubd80\ub974\ub294 \uc218\ub97c \uc758\ubbf8\ud55c\ub2e4. (2 &le; N &le; 50, 0 &le; M &le; N(N-1), 1 &le; a, b, c &le; 100)<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 M\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ud654\uc0b4\ud45c\uc758 \uc2dc\uc791\uc810, \ub05d\uc810 u, v\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; u &ne; v &le; 100) \uc5b4\ub5a4 \ub450 \ud654\uc0b4\ud45c\uc5d0 \ub300\ud574\uc11c\ub3c4 \uc2dc\uc791\uc810\uacfc \ub05d\uc810\uc774 \uc644\uc804\ud788 \uac19\uc9c0\ub294 \uc54a\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc57d \ud604\uc131\uc774\uac00 \ud604\ubbfc\uc774\ub97c \uc774\uae38 \uc218 \uc5c6\ub2e4\uba74 &#39;IMPOSSIBLE&#39;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub807\uc9c0 \uc54a\uc740 \uacbd\uc6b0, \ud604\uc131\uc774\uac00 \ud604\ubbfc\uc774\ub97c \uc774\uae30\uae30 \uc704\ud574 \ud544\uc694\ud55c \ucd5c\uc18c \ud134\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uccab \ubc88\uc9f8 \uc608\uc81c\uc5d0\uc11c\ub294 \ud604\ubbfc\uc774\uac00 1, 2\ub97c \ubc88\uac08\uc544 \ubd80\ub974\uba74 \uac8c\uc784\uc774 \ub05d\ub098\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc5d0 \ud604\ubbfc\uc774\uac00 \uc774\uae34\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc608\uc81c\uc5d0\uc11c\ub294 \uc544\ub798\uc640 \uac19\uc740 \uc804\ub7b5\uc744 \uc138\uc6b0\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub9cc\uc57d \ud604\ubbfc\uc774\uac00 2\ub098 3\uc744 \ubd80\ub978\ub2e4\uba74 \ud55c \ubc88\ub9cc\uc5d0 N\ubc88 \uc6d0\uc73c\ub85c \uac08 \uc218 \uc788\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d \ud604\ubbfc\uc774\uac00 1\uc744 \ubd80\ub978\ub2e4\uba74 4\ubc88 \uc6d0\uc73c\ub85c \uac00\ub294 \uac83\uc774 \ucd5c\uc801\uc774\ub2e4. \ud604\uc131\uc774\uac00 4\ubc88 \uc6d0\uc73c\ub85c \uac04\ub2e4\uba74 \ud604\ubbfc\uc774\uac00 \ub2e4\uc74c \ud134\uc5d0 \ubb34\uc2a8 \uc218\ub97c \ubd80\ub974\ub358\uc9c0 \ud55c \ubc88\uc5d0 N\ubc88 \uc6d0\uc73c\ub85c \uac08 \uc218 \uc788\ub2e4. \ub9cc\uc57d \ud604\uc131\uc774\uac00 5\ubc88 \uc6d0\uc73c\ub85c \uac04\ub2e4\uba74 \ud604\ubbfc\uc774\uac00 2\ub098 3\uc744 \ubd80\ub974\uba74 \ud604\ubbfc\uc774\uac00 \uc774\uae34\ub2e4. \ud604\uc131\uc774\uac00 2\ubc88 \uc6d0\uc73c\ub85c \uac04\ub2e4\uba74 \ud604\uc131\uc774\uac00 \uc774\uae38 \uc218\ub294 \uc788\uc9c0\ub9cc \ub354 \ub9ce\uc740 \ud134\uc744 \uc694\uad6c\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11749\/1.png\" style=\"height:203px; line-height:20.8px; opacity:0.9; text-align:center; width:219px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\ub450 \ubc88\uc9f8 \uc608\uc81c\uc758 \ub9f5<br \/>\r\n&nbsp;<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"11749","problem_lang":"1","title":"Sibling Rivalry","description":"<p>You are playing a game with your elder brother.<\/p>\r\n\r\n<p>First, a number of circles and arrows connecting some pairs of the circles are drawn on the ground. Two of the circles are marked as the start circle and the goal circle.<\/p>\r\n\r\n<p>At the start of the game, you are on the start circle. In each turn of the game, your brother tells you a number, and you have to take that number of steps. At each step, you choose one of the arrows outgoing from the circle you are on, and move to the circle the arrow is heading to. You can visit the same circle or use the same arrow any number of times.<\/p>\r\n\r\n<p>Your aim is to stop on the goal circle after the fewest possible turns, while your brother&rsquo;s aim is to prevent it as long as possible. Note that, in each single turn, you must take the exact number of steps your brother tells you. Even when you visit the goal circle during a turn, you have to leave it if more steps are to be taken.<\/p>\r\n\r\n<p>If you reach a circle with no outgoing arrows before completing all the steps, then you lose the game. You also have to note that, your brother may be able to repeat turns forever, not allowing you to stop after any of them.<\/p>\r\n\r\n<p>Your brother, mean but not too selfish, thought that being allowed to choose arbitrary numbers is not fair. So, he decided to declare three numbers at the start of the game and to use only those numbers.<\/p>\r\n\r\n<p>Your task now is, given the configuration of circles and arrows, and the three numbers declared, to compute the smallest possible number of turns within which you can always finish the game, no matter how your brother chooses the numbers.<\/p>\r\n","input":"<p>The input consists of a single test case, formatted as follows.<\/p>\r\n\r\n<pre>\r\nn m a b c\r\nu<sub>1<\/sub> v<sub>1<\/sub>\r\n.\r\n.\r\n.\r\nu<sub>m<\/sub> v<sub>m<\/sub><\/pre>\r\n\r\n<p>All numbers in a test case are integers. n is the number of circles (2 &le; n &le; 50). Circles arenumbered 1 through n. The start and goal circles are numbered 1 and n, respectively. m is the number of arrows (0 &le; m &le; n(n &minus; 1)). a, b, and c are the three numbers your brother declared (1 &le; a, b, c &le; 100). The pair, u<sub>i<\/sub> and v<sub>i<\/sub>, means that there is an arrow from the circle u<sub>i<\/sub> to the circle v<sub>i<\/sub>. It is ensured that u<sub>i<\/sub> &ne; v<sub>i<\/sub> for all i, and u<sub>i<\/sub> &ne; u<sub>j<\/sub> or v<sub>i<\/sub> &ne; v<sub>j<\/sub> if i &ne; j.<\/p>\r\n","output":"<p>Print the smallest possible number of turns within which you can always finish the game. Print IMPOSSIBLE if your brother can prevent you from reaching the goal, by either making you repeat the turns forever or leading you to a circle without outgoing arrows.<\/p>\r\n","hint":"<p>For Sample Input 1, your brother may choose 1 first, then 2, and repeat these forever. Then you can never finish.<\/p>\r\n\r\n<p>For Sample Input 2 (Figure C.1), if your brother chooses 2 or 3, you can finish with a single turn. If he chooses 1, you will have three options.<\/p>\r\n\r\n<ul>\r\n\t<li>Move to the circle 5. This is a bad idea: Your brother may then choose 2 or 3 and make you lose.<\/li>\r\n\t<li>Move to the circle 4. This is the best choice: From the circle 4, no matter any of 1, 2, or 3 your brother chooses in the next turn, you can finish immediately<\/li>\r\n\t<li>Move to the circle 2. This is not optimal for you. If your brother chooses 1 in the next turn, you cannot finish yet. It will take three or more turns in total.<\/li>\r\n<\/ul>\r\n\r\n<p>In summary, no matter how your brother acts, you can finish within two turns. Thus the answer is 2.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11749\/1.png\" style=\"height:203px; width:219px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure C.1. Sample Input 2<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]