시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

윤이는 유니마을에 거주하는 주민이다. 유니마을은 $1$번부터 $N$번까지 번호가 붙은 $N$개의 건물로 이루어져 있다. 윤이는 그 중 $A$번 건물에 거주하고 있으며, $B$번 건물에 있는 회사로 매일 출퇴근한다.

유니마을은 다음과 같은 구조를 가지고 있다. $N$개의 건물을 잇는 $M$개의 양방향 도로 $R_i$가 있고, 적절한 순서로 도로를 이용하면 임의의 두 건물 사이에 이동이 가능하다. 도로 $R_i$는 서로 다른 $U_i$번 건물과 $V_i$번 건물을 이으며, $R_i$를 거쳐 이동하는 데에는 $T_i$ 만큼의 시간이 소요된다. 한 쌍의 건물을 직접 잇는 도로는 최대 하나이다.

그러던 어느 날, 윤이는 자신이 마법을 쓰면 교통 상황을 바꾸어서 각 도로들을 이동하는데 소모되는 시간을 바꿀 수 있음을 알게 되었다. 윤이는 최대 $K$번 마법을 쓸 수 있는데, 마법을 $k$번 사용하고 나면 모든 $i$에 대해 도로 $R_i$를 이동하는 데 걸리는 시간이 $T_{i, k}$가 된다고 한다. 윤이는 건물에 있을 때만 마법을 사용할 수 있고, 도로를 지나가는 중에 마법을 사용할 수는 없다.

윤이는 마법을 적절히 활용해서 최단 시간으로 회사까지 도착하고자 한다. 윤이를 도와 회사까지 도착하는 데 필요한 최단 시간을 구하시오.

입력

입력의 첫 줄에 $N$과 $M$, 그리고 $A$와 $B$가 주어진다.

다음 $M$개의 줄에 걸쳐 $U_i, V_i, T_i$의 값이 공백을 사이에 두고 주어진다. $(1 \le i \le M)$

다음 줄에 $K$가 주어진다.

다음 $K$개 줄의 $k$번째 줄에는 $T_{1, k}, T_{2, k}, \cdots, T_{M, k}$가 사이에 공백을 두고 주어진다. $(1 \le k \le K)$

출력

윤이가 마법을 적절히 활용했을 때 회사까지 도착하는데 걸리는 최단 시간을 출력한다.

제한

  • $2 \le N \le 1,000$
  • $N-1 \le M \le 2,000$
  • $M \le N(N-1)/2$
  • $1\le A, B, U_i, V_i\le N, A\ne B, U_i \ne V_i$
  • $0 \le K \le 100$
  • $0 \le T_i, T_{i,k} < 10^9$

서브태스크 1 (35점)

$K = 0$

서브태스크 2 (115점)

추가적인 제약 조건이 없다.

예제 입력 1

2 1 2 1
2 1 5
0

예제 출력 1

5

예제 입력 2

3 2 1 3
3 1 5
3 2 5
0

예제 출력 2

5

예제 입력 3

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

예제 출력 3

5

이 예제는 서브태스크 1의 조건을 만족하지 않는다.

[{"problem_id":"20313","problem_lang":"0","title":"\ucd9c\ud1f4\uadfc","description":"<p>\uc724\uc774\ub294 \uc720\ub2c8\ub9c8\uc744\uc5d0 \uac70\uc8fc\ud558\ub294 \uc8fc\ubbfc\uc774\ub2e4. \uc720\ub2c8\ub9c8\uc744\uc740 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc740 $N$\uac1c\uc758 \uac74\ubb3c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uc724\uc774\ub294 \uadf8 \uc911 $A$\ubc88 \uac74\ubb3c\uc5d0 \uac70\uc8fc\ud558\uace0 \uc788\uc73c\uba70, $B$\ubc88 \uac74\ubb3c\uc5d0 \uc788\ub294 \ud68c\uc0ac\ub85c \ub9e4\uc77c \ucd9c\ud1f4\uadfc\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc720\ub2c8\ub9c8\uc744\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uad6c\uc870\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4. $N$\uac1c\uc758 \uac74\ubb3c\uc744 \uc787\ub294 $M$\uac1c\uc758 \uc591\ubc29\ud5a5 \ub3c4\ub85c $R_i$\uac00 \uc788\uace0, \uc801\uc808\ud55c \uc21c\uc11c\ub85c \ub3c4\ub85c\ub97c \uc774\uc6a9\ud558\uba74 \uc784\uc758\uc758 \ub450 \uac74\ubb3c \uc0ac\uc774\uc5d0 \uc774\ub3d9\uc774 \uac00\ub2a5\ud558\ub2e4. \ub3c4\ub85c $R_i$\ub294 \uc11c\ub85c \ub2e4\ub978 $U_i$\ubc88 \uac74\ubb3c\uacfc $V_i$\ubc88 \uac74\ubb3c\uc744 \uc774\uc73c\uba70, $R_i$\ub97c \uac70\uccd0 \uc774\ub3d9\ud558\ub294 \ub370\uc5d0\ub294 $T_i$ \ub9cc\ud07c\uc758 \uc2dc\uac04\uc774 \uc18c\uc694\ub41c\ub2e4. \ud55c \uc30d\uc758 \uac74\ubb3c\uc744 \uc9c1\uc811 \uc787\ub294 \ub3c4\ub85c\ub294 \ucd5c\ub300 \ud558\ub098\uc774\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub7ec\ub358 \uc5b4\ub290 \ub0a0, \uc724\uc774\ub294 \uc790\uc2e0\uc774 \ub9c8\ubc95\uc744 \uc4f0\uba74 \uad50\ud1b5 \uc0c1\ud669\uc744 \ubc14\uafb8\uc5b4\uc11c \uac01 \ub3c4\ub85c\ub4e4\uc744 \uc774\ub3d9\ud558\ub294\ub370 \uc18c\ubaa8\ub418\ub294 \uc2dc\uac04\uc744 \ubc14\uafc0 \uc218 \uc788\uc74c\uc744 \uc54c\uac8c \ub418\uc5c8\ub2e4. \uc724\uc774\ub294 \ucd5c\ub300 $K$\ubc88 \ub9c8\ubc95\uc744 \uc4f8 \uc218 \uc788\ub294\ub370, \ub9c8\ubc95\uc744 $k$\ubc88&nbsp;\uc0ac\uc6a9\ud558\uace0 \ub098\uba74 \ubaa8\ub4e0 $i$\uc5d0 \ub300\ud574 \ub3c4\ub85c $R_i$\ub97c \uc774\ub3d9\ud558\ub294 \ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc774 $T_{i, k}$\uac00 \ub41c\ub2e4\uace0 \ud55c\ub2e4. \uc724\uc774\ub294 \uac74\ubb3c\uc5d0 \uc788\uc744 \ub54c\ub9cc \ub9c8\ubc95\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\uace0, \ub3c4\ub85c\ub97c \uc9c0\ub098\uac00\ub294 \uc911\uc5d0 \ub9c8\ubc95\uc744 \uc0ac\uc6a9\ud560 \uc218\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uc724\uc774\ub294 \ub9c8\ubc95\uc744 \uc801\uc808\ud788 \ud65c\uc6a9\ud574\uc11c \ucd5c\ub2e8 \uc2dc\uac04\uc73c\ub85c \ud68c\uc0ac\uae4c\uc9c0 \ub3c4\ucc29\ud558\uace0\uc790 \ud55c\ub2e4. \uc724\uc774\ub97c \ub3c4\uc640 \ud68c\uc0ac\uae4c\uc9c0 \ub3c4\ucc29\ud558\ub294 \ub370 \ud544\uc694\ud55c \ucd5c\ub2e8 \uc2dc\uac04\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d0 $N$\uacfc $M$, \uadf8\ub9ac\uace0 $A$\uc640 $B$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $M$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 $U_i, V_i, T_i$\uc758 \uac12\uc774 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le i \\le M)$<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0 $K$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $K$\uac1c \uc904\uc758 $k$\ubc88\uc9f8 \uc904\uc5d0\ub294 $T_{1, k}, T_{2, k}, \\cdots, T_{M, k}$\uac00 \uc0ac\uc774\uc5d0 \uacf5\ubc31\uc744 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le k \\le K)$<\/p>\r\n","output":"<p>\uc724\uc774\uac00 \ub9c8\ubc95\uc744 \uc801\uc808\ud788 \ud65c\uc6a9\ud588\uc744 \ub54c \ud68c\uc0ac\uae4c\uc9c0 \ub3c4\ucc29\ud558\ub294\ub370 \uac78\ub9ac\ub294 \ucd5c\ub2e8 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2&nbsp;\\le N \\le 1,000$<\/li>\r\n\t<li>$N-1 \\le M \\le 2,000$<\/li>\r\n\t<li>$M \\le N(N-1)\/2$<\/li>\r\n\t<li>$1\\le A, B, U_i, V_i\\le N, A\\ne B, U_i \\ne V_i$<\/li>\r\n\t<li>$0 \\le K \\le 100$<\/li>\r\n\t<li>$0 \\le T_i, T_{i,k} &lt; 10^9$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$K = 0$<\/p>\r\n","subtask2":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n","sample_explain_3":"<p>\uc774 \uc608\uc81c\ub294 \uc11c\ube0c\ud0dc\uc2a4\ud06c 1\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n"},{"problem_id":"20313","problem_lang":"1","title":"Commute","description":"<p>Yunee is a resident of UNI-town. UNI-town consists of $N$ buildings, numbered from $1$ to $N$. Yunee lives in building $A$&nbsp;and commutes to the company&nbsp;in&nbsp;building $B$&nbsp;every day.<\/p>\r\n\r\n<p>In UNI-town, there are $M$ bidirectional roads $R_i$, each connecting a pair of buildings. It is possible to move from any one building to any other using&nbsp;one or more roads. Road $R_i$ connects two different buildings $U_i$ and $V_i$, and it takes time $T_i$ to travel the road $R_i$. For each pair of buildings, there is at most one road connecting them.<\/p>\r\n\r\n<p>One day, Yunee realized that they can use magic to control the traffic, which changes the time it takes&nbsp;to travel each road. Yunee can use their magic at most $K$ times. After using the&nbsp;magic&nbsp;$k$ times in total, the time it takes&nbsp;to travel the road $R_i$ changes to&nbsp;$T_{i, k}$. Yunee can only use their magic in a building; they cannot use it while traveling a road.<\/p>\r\n\r\n<p>Yunee wants to get to&nbsp;their company in the shortest time by properly utilizing their&nbsp;magic. Help Yunee to find the minimum time required to reach the company.<\/p>\r\n","input":"<p>In the first line, $N$, $M$, $A$, and $B$ are given.<\/p>\r\n\r\n<p>The $i$-th line of the next $M$ lines contains $U_i, V_i, T_i$, separated by whitespace.&nbsp;$(1 \\le i \\le M)$<\/p>\r\n\r\n<p>The next line contains $K$.<\/p>\r\n\r\n<p>The $k$-th line of the next $K$ lines contains&nbsp;$T_{1, k}, T_{2, k}, \\cdots, T_{M, k}$, separated by whitespace.&nbsp;$(1 \\le k \\le K)$<\/p>\r\n","output":"<p>Output the minimum time required to reach the company by properly utilizing Yunee&#39;s magic.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2&nbsp;\\le N \\le 1,000$<\/li>\r\n\t<li>$N-1 \\le M \\le 2,000$<\/li>\r\n\t<li>$M \\le N(N-1)\/2$<\/li>\r\n\t<li>$1\\le A, B, U_i, V_i\\le N, A\\ne B, U_i \\ne V_i$<\/li>\r\n\t<li>$0 \\le K \\le 100$<\/li>\r\n\t<li>$0 \\le T_i, T_{i,k} &lt; 10^9$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$K = 0$<\/p>\r\n","subtask2":"<p>No additional constraints.<\/p>\r\n","sample_explain_3":"<p>Note that this sample data does not satisfy the condition for subtask 1.<\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.