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문제

2015년 구단에서 방출된 셰브첸코는 한때 그의 팬이었던 구단주 로만 아브라히모비치의 도움으로 러시아의 경찰이 되었다.

어느 날 그는 그가 감시를 하고 있는 마피아 조직에서 대규모 이동이 있음을 감지했다. 마피아는 고속도로를 통해서 이동을 하는데 고속도로망은 n개의 톨게이트와 그 사이를 있는 m개의 고속도로로 이루어져있다. 고속도로의 중간에서 밖으로 나가거나 중간으로 들어오지는 못한다고 하자. 즉 모든 이동은 톨게이트와 고속도로를 거쳐서 이루어져야 된다는 것이다. 마피아의 시작점과 도착점이 주어질 때 우리는 몇 개의 톨게이트를 점거해서 마피아가 시작점에서 도착점까지 우리의 점거된 톨게이트를 지나지 않고서는 도착할 수 없게 하고 싶다. 그런데 톨게이트를 점거하는데에는 각각의 톨게이트마다 고유한 비용이 든다.

이때 점거비를 최소화 하며 마피아의 움직임을 막기 위해 점거해야되는 도시들을 출력하여라.

입력

첫 줄에는 톨게이트의 개수 n과 고속도로의 개수 m이 주어진다.(1 ≤ n ≤ 200, 1 ≤ m ≤ 20000) 톨게이트의 번호는 1부터 n까지로 주어진다고 할 때, 다음 줄에는 마피아의 시작점과 도착점이 주어진다. 그리고 그 다음 n개의 줄에는 각 톨게이트별 점거비용이 나온다. 그 뒤 m개의 줄에는 톨게이트를 잇는 고속도로들이 주어진다. 점거비용은 10,000,000보다 작거나 같은 자연수이다.

출력

점거비를 최소화 하며 마피아의 움직임을 막기 위해 점거해야되는 도시들을 오름차순으로 출력하여라.

예제 입력 1

5 6
5 3
2
4
8
3
10
1 5
1 2
2 4
4 5
2 3
3 4

예제 출력 1

1 4
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The police knows the date of the transport and they know that the transport will use the national highway network.<\/p>\r\n\r\n<p>The highway network consists of two-way highway segments, each segment directly connecting two distinct toll stations. A toll station may be connected with many other stations. A vehicle can enter or exit the highway network at toll stations only. The ma\ufb01a transport is known to enter the highways at the toll station closest to the harbour and leave it at the toll station closest to the warehouse (it will not leave and re-enter the highways in between). Special police squads are to be located in selected toll stations. When the transport enters a toll station under surveillance, it will be caught by the police.<\/p>\r\n\r\n<p>From this point of view, the easiest choice would be to place the police squad either at the entry point or the exit point of the transport. However, controlling each toll station has a certain cost, which may vary from station to station. The police wants to keep the overall cost as low as possible, so they need to identify a minimal controlling set of toll stations, which satis\ufb01es the two conditions:<\/p>\r\n\r\n<ul>\r\n\t<li>all tra\ufb03c from the harbour to the warehouse must pass through at least one station from that set,<\/li>\r\n\t<li>the cost of monitoring these stations (i.e. the sum of their individual monitoring costs) is minimal.<\/li>\r\n<\/ul>\r\n\r\n<p>You may assume that it is possible to get from the harbour to the warehouse using the highways.<\/p>\r\n\r\n<p>Write a program, that:<\/p>\r\n\r\n<ul>\r\n\t<li>reads the description of the highway network, the monitoring costs and the locations of the entry and exit points of the transport from the standard input,<\/li>\r\n\t<li>\ufb01nds a minimal controlling set of toll stations,<\/li>\r\n\t<li>writes this set to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>The \ufb01rst line of the standard input contains two integers n and m (2 &le; n &le; 200 , 1 &le; m &le; 20000) &mdash; the number of toll stations and the number of direct highway segments. The toll stations are numbered from 1 to n.<\/p>\r\n\r\n<p>The second line contains two integers a and b (1 &le; a, b &le; n, a &ne; b) &mdash; the numbers of the toll stations closest to the harbour and to the warehouse, respectively.<\/p>\r\n\r\n<p>The following n lines describe the monitoring costs. The i-th of these lines (for 1 &le; i &le; n) contains one integer &mdash; the monitoring cost of the i-th station (which is positive number not exceeding 10 000 000 ).<\/p>\r\n\r\n<p>The following m lines describe the highway network. The j-th of these lines (for 1 &le; j &le; m) contains two integers x and y (1 &le; x &lt; y &le; n), indicating that there is a direct highway segment between toll stations numbered x and y. Each highway segment is listed once.<\/p>\r\n","output":"<p>The only line of the output should contain the numbers of toll stations in a minimal controlling set, given in increasing order, separated by single spaces. If there is more than one minimal controlling set, your program may output anyone of them.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > Baltic Olympiad in Informatics > BOI 2008 6번