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문제

Nikola는 Bit 마을에 살고 있고 Hex 마을에 사는 Anita의 남자친구이다. Nikola는 주변 지도를 아주 잘 알고 있어서 두 마을 사이의 최단 경로를 찾았다. 그리고 이 경로를 운 좋은 경로라고 부르기로 했다. 주변 지도는 서로 다른 마을을 잇는 양방향 도로의 집합으로 표현된다.

어떤 날, 이 나라의 대통령이 도로에 공사를 하기로 했다. 나라의 교통을 유지하기 위하여, 오직 하루에 하나의 도로만 닫기로 했다.

운 좋은 경로에 있는 도로에 대해서, Nikola는 그 도로가 닫혔을 때 Anita와의 최단 경로의 길이를 알고 싶어 한다.

입력

입력의 첫째 줄은 4개의 정수로 이루어진다: n - 도시의 개수; m - 도로의 개수; a - Bit 마을(Nikola가 살고 있는 마을)의 번호; b - Hex 마을(Anita가 살고 있는 마을)의 번호.

마을들에는 1부터 n까지의 번호가 부여된다. 다음 m개의 줄은 u, v, w 3개의 정수를 포함하며 도로에 대한 정보를 준다: 마을 u와 마을 v는 길이 w의 도로로 이어져 있다.

입력의 마지막 줄은 숫자 k와 k개의 숫자(v1(=a), v2, …, vk(=b))로 이루어 지고, Nikola의 운 좋은 경로를 나타낸다.

출력

각각의 정수 t = 1 … k – 1에 대해, 각 줄마다 도로 (vt, vt+1)가 닫혔을 경우에 마을 a와 마을 b 사이의 최단 경로의 길이를 출력하라. 만약 경로가 없다면 -1을 출력하라.

제한

  • 1 ≤ n ≤ 2000, 1 ≤ m ≤ 100.000
  • 1 ≤ a, b ≤ n
  • 1 ≤ w ≤ 100.000
  • 서로 다른 두 도시 사이에는 최대 하나의 도로가 존재한다.
  • 주어진 경로는 마을 a와 마을 b 사이의 최단 경로 중 하나이다.

예제 입력 1

5 6 1 5
1 2 1
2 3 3
2 5 100
3 4 3
3 5 5
4 5 3
4 1 2 3 5

예제 출력 1

-1
101
10

힌트

[{"problem_id":"5250","problem_lang":"0","title":"\ucd5c\ub2e8 \uacbd\ub85c\ub4e4","description":"<p>Nikola\ub294 Bit \ub9c8\uc744\uc5d0 \uc0b4\uace0 \uc788\uace0 Hex \ub9c8\uc744\uc5d0&nbsp;\uc0ac\ub294 Anita\uc758 \ub0a8\uc790\uce5c\uad6c\uc774\ub2e4. Nikola\ub294 \uc8fc\ubcc0 \uc9c0\ub3c4\ub97c \uc544\uc8fc \uc798 \uc54c\uace0 \uc788\uc5b4\uc11c \ub450 \ub9c8\uc744 \uc0ac\uc774\uc758 \ucd5c\ub2e8 \uacbd\ub85c\ub97c \ucc3e\uc558\ub2e4. \uadf8\ub9ac\uace0 \uc774 \uacbd\ub85c\ub97c \uc6b4 \uc88b\uc740 \uacbd\ub85c\ub77c\uace0 \ubd80\ub974\uae30\ub85c \ud588\ub2e4. \uc8fc\ubcc0 \uc9c0\ub3c4\ub294 \uc11c\ub85c \ub2e4\ub978 \ub9c8\uc744\uc744 \uc787\ub294 \uc591\ubc29\ud5a5 \ub3c4\ub85c\uc758 \uc9d1\ud569\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \ub0a0, \uc774 \ub098\ub77c\uc758 \ub300\ud1b5\ub839\uc774 \ub3c4\ub85c\uc5d0 \uacf5\uc0ac\ub97c \ud558\uae30\ub85c \ud588\ub2e4. \ub098\ub77c\uc758 \uad50\ud1b5\uc744 \uc720\uc9c0\ud558\uae30 \uc704\ud558\uc5ec, \uc624\uc9c1 \ud558\ub8e8\uc5d0 \ud558\ub098\uc758 \ub3c4\ub85c\ub9cc \ub2eb\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uc6b4 \uc88b\uc740 \uacbd\ub85c\uc5d0 \uc788\ub294 \ub3c4\ub85c\uc5d0 \ub300\ud574\uc11c, Nikola\ub294 \uadf8 \ub3c4\ub85c\uac00 \ub2eb\ud614\uc744 \ub54c Anita\uc640\uc758 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \uc54c\uace0 \uc2f6\uc5b4 \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab\uc9f8 \uc904\uc740 4\uac1c\uc758 \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4: n - \ub3c4\uc2dc\uc758 \uac1c\uc218; m - \ub3c4\ub85c\uc758 \uac1c\uc218; a - Bit \ub9c8\uc744(Nikola\uac00 \uc0b4\uace0 \uc788\ub294 \ub9c8\uc744)\uc758 \ubc88\ud638; b - Hex \ub9c8\uc744(Anita\uac00 \uc0b4\uace0 \uc788\ub294 \ub9c8\uc744)\uc758 \ubc88\ud638.<\/p>\r\n\r\n<p>\ub9c8\uc744\ub4e4\uc5d0\ub294 1\ubd80\ud130 n\uae4c\uc9c0\uc758 \ubc88\ud638\uac00 \ubd80\uc5ec\ub41c\ub2e4. \ub2e4\uc74c m\uac1c\uc758 \uc904\uc740 u, v, w 3\uac1c\uc758 \uc815\uc218\ub97c \ud3ec\ud568\ud558\uba70 \ub3c4\ub85c\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \uc900\ub2e4: \ub9c8\uc744 u\uc640 \ub9c8\uc744 v\ub294 \uae38\uc774 w\uc758 \ub3c4\ub85c\ub85c \uc774\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc740 \uc22b\uc790 k\uc640 k\uac1c\uc758 \uc22b\uc790(v<sub>1<\/sub>(=a), v<sub>2<\/sub>, &hellip;, v<sub>k<\/sub>(=b))\ub85c \uc774\ub8e8\uc5b4 \uc9c0\uace0, Nikola\uc758 \uc6b4 \uc88b\uc740 \uacbd\ub85c\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc815\uc218 t = 1 &hellip; k &ndash; 1\uc5d0 \ub300\ud574, \uac01 \uc904\ub9c8\ub2e4 \ub3c4\ub85c (v<sub>t<\/sub>, v<sub>t+1<\/sub>)\uac00 \ub2eb\ud614\uc744 \uacbd\uc6b0\uc5d0 \ub9c8\uc744 a\uc640 \ub9c8\uc744 b \uc0ac\uc774\uc758 \ucd5c\ub2e8 \uacbd\ub85c\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud558\ub77c. \ub9cc\uc57d \uacbd\ub85c\uac00 \uc5c6\ub2e4\uba74 -1\uc744 \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","hint":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/8b9e4508-3f71-4f17-8c55-10b83e99c320\/-\/preview\/\" style=\"width: 333px; height: 127px;\" \/><\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>1 &le; n &le; 2000, 1 &le; m &le; 100.000<\/li>\r\n\t<li>1 &le; a, b &le; n<\/li>\r\n\t<li>1 &le; w &le; 100.000<\/li>\r\n\t<li>\uc11c\ub85c \ub2e4\ub978 \ub450 \ub3c4\uc2dc \uc0ac\uc774\uc5d0\ub294 \ucd5c\ub300 \ud558\ub098\uc758 \ub3c4\ub85c\uac00 \uc874\uc7ac\ud55c\ub2e4.<\/li>\r\n\t<li>\uc8fc\uc5b4\uc9c4 \uacbd\ub85c\ub294 \ub9c8\uc744 a\uc640 \ub9c8\uc744 b \uc0ac\uc774\uc758 \ucd5c\ub2e8 \uacbd\ub85c \uc911 \ud558\ub098\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n"},{"problem_id":"5250","problem_lang":"1","title":"Shortest paths","description":"<p>Nikola lives in Bittown and he is in love with his girlfriend Anita from a town called Hextown. Nikola knows the country map very well, and he found the shortest path between these two towns. He calls this path lucky path. The map of the country can be described as a collection of towns connected with bidirectional roads.<\/p>\r\n\r\n<p>One day the president of this country decided that there are going to be some works on the roads. In order to uphold the traffic in the country, only one road is going to be closed per day.&nbsp;<\/p>\r\n\r\n<p>For each road on the lucky path, Nikola wants to know the length of the shortest path between Anita and him if that road is closed.<\/p>\r\n","input":"<p>The first line of input contains four integers: n &mdash; the number of cities; m &mdash; the number of roads between these towns; a &mdash; index of town Bittown where Nikola lives; b &mdash; the index of town Hextown where Anita lives. Towns are indexed with numbers 1, 2,&hellip;, n. Next m lines specify roads: each line contains three integers: u, v and w &ndash; there exist road between towns u and v with length w. Last line of the input contains number k followed by k numbers a = v<sub>1<\/sub>, v<sub>2<\/sub>, &hellip;, v<sub>k<\/sub> = b &ndash; the lucky path that Nikola uses.&nbsp;<\/p>\r\n","output":"<p>For every integer t = 1 &hellip; k &ndash; 1, in separate line, print the length of the shortest path between cities a and b, if the road (v<sub>t<\/sub>, v<sub>t+1<\/sub>) is closed. If there is no such path, output &ldquo;-1&rdquo; without quotes.&nbsp;<\/p>\r\n","hint":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/8b9e4508-3f71-4f17-8c55-10b83e99c320\/-\/preview\/\" style=\"width: 333px; height: 127px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1. Description of the example<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>1 &le; n &le; 2000, 1 &le; m &le; 100.000<\/li>\r\n\t<li>1 &le; a, b &le; n<\/li>\r\n\t<li>1 &le; w &le; 100.000<\/li>\r\n\t<li>There is at most one road between each pair of cities.<\/li>\r\n\t<li>You may assume that the given path is one of the shortest paths that connects given two cities a and b.&nbsp;<\/li>\r\n<\/ul>\r\n"}]

출처

Olympiad > Balkan Olympiad in Informatics > BOI 2012 2번