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문제

어느 나라에는, N개의 도시가 있다. 각각 1부터 N까지 번호가 매겨저 있다. 한 엔지니어는 모든 도시를 연결하는 길을 깔아야 한다. 즉, 어떤 도시에서라도 모든 도시를 갈 수 있고, 여러 도시를 통과할 수도 있어야 한다. 엔지니어가 속한 팀은 몇몇 노선을 정하기 위해 설문조사를 하였다.(두 도시 사이의 후보 도로). 노선은 서로 두 도시 사이에 양방향으로 연결되어있다. 그는 설문조사 한 노선에 특정 요금을 매기고 양방향 길을 지을 수 있다.(길이 짧을수록 비용은 더 싸다.)

이 엔지니어는 미리 도로 시스템을 구축한 적이 한번도 없다. 그는 그냥 그가 원하는 길을 하나 골라, 모든 도시가 연결될 때까지 짓는다.

기사는 p 도시에서 q 도시까지 연결되는 길을 지으려고 한다.

비용을 줄이기 위해서 들어온 정부의 압력으로, 길을 지어야 하는지 짓지 말아야 하는지를 나타내는 프로그램을 작성하려 한다.

입력

첫 번째 줄에는 테스트 케이스 T ≤ 10 이 들어온다.

테스트 케이스는 모두 정수 N, M, p 와 q가 들어와야 한다. N(2 ≤ N ≤ 10 000)은 설문조사된 길이다. p와 q에 표시해야 하는 노선은(1 ≤ p ≤ N) (1 ≤ q ≤ N) 두 도시 사이에, 즉 엔지니어가 그가 길을 지을 수 있는지를 표시한다.

그런 다음, 다음 M 라인은 각각의 3개의 숫자인 U, V, W (1 U는 1 000 400 ≤ w ≤ N, 1 ≤ V의 ≤의 N을, ≤ ≤) U 사이의 w 길이의 양방향 경로가 있음을 나타냅니다 그리고 절 현재 시스템에있는 각 도로의 길이는 고유합니다. 그리고, 두 도시 사이에 하나의 가능한도가있다.입력은 적어도 하나의 도로 시스템이 두 도시 간의 경로가 있는지 보장한다. 모든 숫자는 정수이다.

출력

테스트 케이스에서 만약 엔지니어가 p-q 길을 가장 짧게 지을 수 있다면 YES를 출력한다. 불가능하다면 NO를 출력한다.

예제 입력 1

3
2 1 1 2
1 2 4
3 3 2 3
1 2 1
1 3 2
2 3 3
4 5 3 4
1 2 1
1 3 3
3 4 2
1 4 4
4 2 5

예제 출력 1

YES
NO
YES
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N(2 &le; N &le; 10 000)\uc740 \uc124\ubb38\uc870\uc0ac\ub41c \uae38\uc774\ub2e4. p\uc640 q\uc5d0 \ud45c\uc2dc\ud574\uc57c \ud558\ub294 \ub178\uc120\uc740(1 &le; p &le; N) (1 &le; q &le; N) \ub450 \ub3c4\uc2dc \uc0ac\uc774\uc5d0, \uc989 \uc5d4\uc9c0\ub2c8\uc5b4\uac00 \uadf8\uac00 \uae38\uc744 \uc9c0\uc744 \uc218 \uc788\ub294\uc9c0\ub97c \ud45c\uc2dc\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub7f0 \ub2e4\uc74c, \ub2e4\uc74c M \ub77c\uc778\uc740 \uac01\uac01\uc758 3\uac1c\uc758 \uc22b\uc790\uc778&nbsp;U, V, W (1 U\ub294 1 000 400 &le; w &le; N, 1 &le; V\uc758 &le;\uc758 N\uc744, &le; &le;) U \uc0ac\uc774\uc758 w \uae38\uc774\uc758 \uc591\ubc29\ud5a5 \uacbd\ub85c\uac00 \uc788\uc74c\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4 \uadf8\ub9ac\uace0 \uc808 \ud604\uc7ac \uc2dc\uc2a4\ud15c\uc5d0\uc788\ub294 \uac01 \ub3c4\ub85c\uc758 \uae38\uc774\ub294 \uace0\uc720\ud569\ub2c8\ub2e4. \uadf8\ub9ac\uace0, \ub450 \ub3c4\uc2dc \uc0ac\uc774\uc5d0 \ud558\ub098\uc758 \uac00\ub2a5\ud55c\ub3c4\uac00\uc788\ub2e4.\uc785\ub825\uc740 \uc801\uc5b4\ub3c4 \ud558\ub098\uc758 \ub3c4\ub85c \uc2dc\uc2a4\ud15c\uc774 \ub450 \ub3c4\uc2dc \uac04\uc758 \uacbd\ub85c\uac00 \uc788\ub294\uc9c0 \ubcf4\uc7a5\ud55c\ub2e4. \ubaa8\ub4e0 \uc22b\uc790\ub294 \uc815\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c \ub9cc\uc57d \uc5d4\uc9c0\ub2c8\uc5b4\uac00 p-q \uae38\uc744 \uac00\uc7a5 \uc9e7\uac8c \uc9c0\uc744 \uc218 \uc788\ub2e4\uba74 YES\ub97c \ucd9c\ub825\ud55c\ub2e4. \ubd88\uac00\ub2a5\ud558\ub2e4\uba74 NO\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9344","problem_lang":"1","title":"Road","description":"<p>In one country, there are N cities, numbered 1 to N. A civil engineer has to build public roads that connect all the cities together, i.e., it must be possible to travel from all cities to any other cities, maybe going through multiple cities. His team has surveyed several routes (candidate road between any two cities). Each route is a bidirectional connection between two cities. He can build a bi-directional road on the surveyed route for a specific cost (The shorter the route is the cheaper the road).<\/p>\r\n\r\n<p>This engineer has never planned a road system in advance. He would just pick one of the routes based on his preference, and build a road until all the cities are connected.&nbsp;<\/p>\r\n\r\n<p>Right now this engineer is going to build a road from the city p to the city q. With pressure from the government to reduce the cost, he asks you to write a program to decide, if he should build this road or not. Your program should say yes if the building of this road guaranteed that it can be part of the shortest road system that connects all cities together. Otherwise, your program should say no.&nbsp;<\/p>\r\n","input":"<p>First line of input is a number of test cases T &le; 10.&nbsp;<\/p>\r\n\r\n<p>Each test case start with a line contains 4 integers N, M, p, and q. N (2 &le; N &le; 10 000) is the number of cities in this road system. M (1 &le; M &le; 20 000) is the number of surveyed routes. p and q (1 &le; p &le; N and 1 &le; q &le; N) indicate the route between two cities, that the engineer asks if he can build a road or not.&nbsp;<\/p>\r\n\r\n<p>Then, the each of the following M lines contains 3 numbers u, v, and w (1 &le; u &le; N, 1 &le; v &le; N, 1 &le; w &le; 400 000) indicates that there are the bidirectional route of length w between u and v. The length of each road in the current system is unique. And, there is only one possible road between two cities. The input guarantees that at least one road system has a route between any two cities. All numbers are integer<\/p>\r\n","output":"<p>For each test case, display YES if the engineer can build a road p-q as part of the shortest road system. Otherwise, print NO.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]