시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 256 MB 140 57 30 47.619%

문제

사회에 불만이 많은 지용이는 미적분학 교과서를 적당히 찢어서, 한 사람이 충분히 탈 만한 두께 K의 뗏목을 만들었다.

지용이는 이제 A 항구에서 출발해서 무인도 B에 자신의 제국을 건설하기 위해 멀고 먼 여행을 떠날 계획이다. (1 ≤ A, B ≤ N, A ≠ B)

바다에는 N개의 섬이 있고 M개의 바닷길이 있으며, 바닷길 외의 길로는 갈 수가 없으며 지용이는 A에서 B로 가는 동안 섬들을 거쳐가면서 항해할 계획이다.

각 바닷길은 지나가는 데 걸리는 시간 ti, 뗏목을 깎아내리는 정도 hi (cm) 를 가지고 있으며, 만약에 도착하기 전에 뗏목이 0cm 이하의 두께를 가지게 된다면 - 달리 말해서 경로 상의 hi의 합이 K 이상이 된다면, 수영을 못하는 지용이의 목숨을 보장하지 못할수도 있다(!)

지용이는 가장 빠른 시간 내에 A에서 B 지점까지 안전하게 가기를 원한다. 지용이를 도와 그러한 길의 길이를 출력해주자.

입력

첫 번째 줄에는 정수 K, N, M (1 ≤ K ≤ 200; 2 ≤ N ≤ 2000; 1 ≤ M ≤ 10000)이 주어진다.

이 후 M개의 줄에 각 바닷길의 정보가 A, B, ti, hi (1 ≤ A,B ≤ N; 1 ≤ ti ≤ 105; 0 ≤ hi ≤ 200) 형태로 주어진다. 이는 A와 B를 잇는 바닷길이 존재하며, 이 바닷길은 ti의 시간이 걸리며 hi 만큼 뗏목을 깎아내린다는 것을 의미한다. A ≠ B임이 보장된다.

마지막 줄에는 시작점과 도착점인 A, B가 주어진다. (1 ≤ A, B ≤ N; A ≠ B)

출력

지용이가 안전하게 A에서 B에서 항해할 수 있다면 그 때 걸리는 시간을, 그럴 수 없다면 -1을 출력한다.

예제 입력 1

10 4 7
1 2 4 4
1 3 7 2
3 1 8 1
3 2 2 2
4 2 1 6
3 4 1 1
1 4 6 12
1 4

예제 출력 1

7

예제 입력 2

3 3 3
1 2 5 1
3 2 8 2
1 3 1 3
1 3

예제 출력 2

-1
[{"problem_id":"10776","problem_lang":"0","title":"\uc81c\uad6d","description":"<p>\uc0ac\ud68c\uc5d0 \ubd88\ub9cc\uc774 \ub9ce\uc740 \uc9c0\uc6a9\uc774\ub294 \ubbf8\uc801\ubd84\ud559 \uad50\uacfc\uc11c\ub97c \uc801\ub2f9\ud788 \ucc22\uc5b4\uc11c, \ud55c \uc0ac\ub78c\uc774 \ucda9\ubd84\ud788 \ud0c8 \ub9cc\ud55c \ub450\uaed8 K\uc758 \ub5cf\ubaa9\uc744 \ub9cc\ub4e4\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uc9c0\uc6a9\uc774\ub294 \uc774\uc81c A \ud56d\uad6c\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c \ubb34\uc778\ub3c4 B\uc5d0 \uc790\uc2e0\uc758 \uc81c\uad6d\uc744 \uac74\uc124\ud558\uae30 \uc704\ud574 \uba40\uace0 \uba3c \uc5ec\ud589\uc744 \ub5a0\ub0a0 \uacc4\ud68d\uc774\ub2e4. (1 &le; A, B &le; N, A &ne; B)<\/p>\r\n\r\n<p>\ubc14\ub2e4\uc5d0\ub294 N\uac1c\uc758 \uc12c\uc774 \uc788\uace0 M\uac1c\uc758 \ubc14\ub2f7\uae38\uc774 \uc788\uc73c\uba70, \ubc14\ub2f7\uae38 \uc678\uc758 \uae38\ub85c\ub294 \uac08 \uc218\uac00 \uc5c6\uc73c\uba70 \uc9c0\uc6a9\uc774\ub294 A\uc5d0\uc11c B\ub85c \uac00\ub294 \ub3d9\uc548 \uc12c\ub4e4\uc744 \uac70\uccd0\uac00\uba74\uc11c \ud56d\ud574\ud560 \uacc4\ud68d\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ubc14\ub2f7\uae38\uc740 \uc9c0\ub098\uac00\ub294 \ub370 \uac78\ub9ac\ub294 \uc2dc\uac04 ti, \ub5cf\ubaa9\uc744 \uae4e\uc544\ub0b4\ub9ac\ub294 \uc815\ub3c4 h<sub>i<\/sub> (cm) \ub97c \uac00\uc9c0\uace0 \uc788\uc73c\uba70, \ub9cc\uc57d\uc5d0 \ub3c4\ucc29\ud558\uae30 \uc804\uc5d0 \ub5cf\ubaa9\uc774 0cm \uc774\ud558\uc758 \ub450\uaed8\ub97c \uac00\uc9c0\uac8c \ub41c\ub2e4\uba74 - \ub2ec\ub9ac \ub9d0\ud574\uc11c \uacbd\ub85c \uc0c1\uc758 h<sub>i<\/sub>\uc758 \ud569\uc774 K \uc774\uc0c1\uc774 \ub41c\ub2e4\uba74, \uc218\uc601\uc744 \ubabb\ud558\ub294 \uc9c0\uc6a9\uc774\uc758 \ubaa9\uc228\uc744 \ubcf4\uc7a5\ud558\uc9c0 \ubabb\ud560\uc218\ub3c4 \uc788\ub2e4(!)<\/p>\r\n\r\n<p>\uc9c0\uc6a9\uc774\ub294 \uac00\uc7a5 \ube60\ub978 \uc2dc\uac04 \ub0b4\uc5d0 A\uc5d0\uc11c B \uc9c0\uc810\uae4c\uc9c0 \uc548\uc804\ud558\uac8c \uac00\uae30\ub97c \uc6d0\ud55c\ub2e4. \uc9c0\uc6a9\uc774\ub97c \ub3c4\uc640 \uadf8\ub7ec\ud55c \uae38\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud574\uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc815\uc218 K, N, M (1 &le; K &le; 200; 2 &le; N &le; 2000; 1 &le; M &le; 10000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ud6c4 M\uac1c\uc758 \uc904\uc5d0 \uac01 \ubc14\ub2f7\uae38\uc758 \uc815\ubcf4\uac00 A, B, t<sub>i<\/sub>, hi (1 &le; A,B &le; N; 1 &le; t<sub>i<\/sub> &le; 10<sup>5<\/sup>; 0 &le; h<sub>i<\/sub> &le; 200) \ud615\ud0dc\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 A\uc640 B\ub97c \uc787\ub294 \ubc14\ub2f7\uae38\uc774 \uc874\uc7ac\ud558\uba70, \uc774 \ubc14\ub2f7\uae38\uc740 t<sub>i<\/sub>\uc758 \uc2dc\uac04\uc774 \uac78\ub9ac\uba70 h<sub>i<\/sub> \ub9cc\ud07c \ub5cf\ubaa9\uc744 \uae4e\uc544\ub0b4\ub9b0\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud55c\ub2e4. A &ne; B\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 \uc2dc\uc791\uc810\uacfc \ub3c4\ucc29\uc810\uc778 A, B\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; A, B &le; N; A &ne; B)<\/p>\r\n","output":"<p>\uc9c0\uc6a9\uc774\uac00 \uc548\uc804\ud558\uac8c A\uc5d0\uc11c B\uc5d0\uc11c \ud56d\ud574\ud560 \uc218 \uc788\ub2e4\uba74 \uadf8 \ub54c \uac78\ub9ac\ub294 \uc2dc\uac04\uc744, \uadf8\ub7f4 \uc218 \uc5c6\ub2e4\uba74 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10776","problem_lang":"1","title":"Convex Hull","description":"<p>You are travelling on a ship in an archipelago. The ship has a convex hull which is K centimetres thick. The archipelago has N islands, numbered from 1 to N. There are M sea routes amongst them, where the ith route runs directly between two different islands a<sub>i<\/sub> and b<sub>i<\/sub> (1 &le; a<sub>i<\/sub>, b<sub>i<\/sub> &le; N), takes t<sub>i<\/sub> minutes to travel along in either direction, and has rocks that wear down the ship&rsquo;s hull by h<sub>i<\/sub> centimetres. There may be multiple routes running between a pair of islands.<\/p>\r\n\r\n<p>You would like to travel from island A to a different island B (1 &le; A, B &le; N) along a sequence of sea routes, such that your ship&rsquo;s hull remains intact &ndash; in other words, such that the sum of the routes&rsquo; hi values is strictly less than K.<\/p>\r\n\r\n<p>Additionally, you are in a hurry, so you would like to minimize the amount of time necessary to reach island B from island A. It may not be possible to reach island B from island A, however, either due to insufficient sea routes or the having the ship&rsquo;s hull wear out.<\/p>\r\n","input":"<p>The first line of input contains three integers K, N and M (1 &le; K &le; 200, 2 &le; N &le; 2000, 1 &le; M &le; 10000), each separated by one space.<\/p>\r\n\r\n<p>The next M lines each contain 4 integers a<sub>i<\/sub> b<sub>i<\/sub> t<sub>i<\/sub> and h<sub>i<\/sub> (1 &le; a<sub>i<\/sub>, b<sub>i<\/sub> &le; N, 1 &le; t<sub>i<\/sub> &le; 10<sup>5<\/sup>, 0 &le; h<sub>i<\/sub> &le; 200), each separated by one space. The ith line in this set of M lines describes the ith sea route (which runs from island a<sub>i<\/sub> to island b<sub>i<\/sub>, takes t<sub>i<\/sub> minutes and wears down the ship&rsquo;s hull by h<sub>i<\/sub> centimetres). Notice that a<sub>i<\/sub> &ne; b<sub>i<\/sub> (that is, the ends of a sea route are distinct islands).<\/p>\r\n\r\n<p>The last line of input contains two integers A and B (1 &le; A, B &le; N; A &ne; B), the islands between which we want to travel.<\/p>\r\n\r\n<p>For 20% of marks for this question, K = 1 and N &le; 200. For another 20% of the marks for this problem, K = 1 and N &le; 2000.<\/p>\r\n","output":"<p>Output a single integer: the integer representing the minimal time required to travel from A to B without wearing out the ship&rsquo;s hull, or &minus;1 to indicate that there is no way to travel from A to B without wearing out the ship&rsquo;s hull.<\/p>\r\n","hint":"<p>Explanation of Output for Sample Input 1<\/p>\r\n\r\n<p>The path of length 1 from 1 to 4 would wear out the hull of the ship. The three paths of length 2 ([1, 2, 4] and [1, 3, 4] two different ways) take at least 8 minutes. The path [1, 2, 3, 4] takes 7 minutes and only wears down the hull by 7 centimetres, whereas the path [1, 3, 2, 4] takes 13 minutes and wears down the hull by 5 centimetres.<\/p>\r\n\r\n<p>Explanation of Output for Sample Input 2<\/p>\r\n\r\n<p>The direct path [1, 3] wears down the hull to 0, as does the path [1, 2, 3].<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]