문제
서울과학고의 기숙사는 $N$개의 방과 서로 다른 두 방을 연결하는 $N-1$개의 복도로 이루어진 트리 형태로 표현할 수 있다. 모든 복도는 양방향으로 이동할 수 있고, 복도를 이용해 모든 방 사이를 이동할 수 있다. 하나의 복도를 통과하는 데 걸리는 시간은 1ドル$이다.
민규는 $K$명의 친구에게 컵라면을 끓여주려고 한다. 현재 민규는 1ドル$번 방에 있으며, 민규를 포함한 모든 친구들은 서로 다른 방에 있다.
이를 위해 민규는 모든 친구들에게 뜨거운 물을 전달할 것이다. 뜨거운 물은 민규가 있는 1ドル$번 방의 정수기에서만 얻을 수 있다. 또한, 민규는 매우 큰 보온병을 가지고 있어 물을 한 번만 받아도 모든 친구에게 줄 수 있는 충분한 양의 물을 받을 수 있다.
라면을 끓이는 행동은 위험한 행동이다. 사감 선생님께 걸리면 벌점을 받을 수 있기 때문이다. 민규는 위험을 최대한 줄이기 위해 가장 마지막으로 뜨거운 물을 배달한 시각이 최대한 빠른 방법으로 $K$개의 방을 방문할 것이다.
민규가 $K$개의 방을 방문하는 방법을 더 자세히 설명하면 다음과 같다.
- 민규는 물을 받기 전, $K$명의 친구들이 있는 방을 미리 확인한다.
- 민규는 시각 0ドル$에 1ドル$번 방에서 물을 받고 출발해, 가장 마지막으로 뜨거운 물을 배달하는 친구에게 걸리는 시간을 최소화하는 방법으로 $K$개의 방을 방문할 것이다.
- 시간을 계산할 때는 민규가 복도를 이동하는 시간만 고려한다. 친구에게 물을 주는 시간이나 정수기에서 물을 뜨는 시간 등은 무시한다. 민규가 물을 다 주고 자신의 방으로 돌아가는 시간 역시 무시한다.
민규는 친구들이 있는 방을 확인하기 전에, 친구들에게 물을 배달하는 데 시간이 얼마나 걸릴지 예측하려고 한다. $K$명의 친구들이 있는 방을 고르는 $\binom{N-1}{K}$가지 경우에 대해, 마지막으로 물을 배달하는 시각의 합을 구해 주자.
출력
친구들이 있는 방을 고르는 $\binom{N-1}{K}$가지 경우에 대해 마지막으로 물을 배달하는 시각의 합을 10ドル^9 + 7$으로 나눈 나머지를 출력하여라.
제한
- 2ドル\le N\le 10^5$
- 1ドル\le K\le N-1$
- 1ドル\le U_i\le N$ $(1\le i<N)$
- 1ドル\le V_i\le N$ $(1\le i<N)$
- $U_i\ne V_i$ $(1\le i<N)$
- 입력으로 주어지는 서울과학고의 구조는 트리임이 보장된다.
서브태스크
| 번호 | 배점 | 제한 | | 1 | 10 | $N \le 10$
|
| 2 | 40 | $N \le 10^3$
|
| 3 | 50 | 추가 제한 조건이 없다.
|
[{"problem_id":"31070","problem_lang":"0","title":"\ub77c\uba74 \ubc30\ub2ec\ud558\uae30","description":"<p>\uc11c\uc6b8\uacfc\ud559\uace0\uc758 \uae30\uc219\uc0ac\ub294 $N$\uac1c\uc758 \ubc29\uacfc \uc11c\ub85c \ub2e4\ub978 \ub450 \ubc29\uc744 \uc5f0\uacb0\ud558\ub294 $N-1$\uac1c\uc758 \ubcf5\ub3c4\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ud2b8\ub9ac \ud615\ud0dc\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4. \ubaa8\ub4e0 \ubcf5\ub3c4\ub294 \uc591\ubc29\ud5a5\uc73c\ub85c \uc774\ub3d9\ud560 \uc218 \uc788\uace0, \ubcf5\ub3c4\ub97c \uc774\uc6a9\ud574 \ubaa8\ub4e0 \ubc29 \uc0ac\uc774\ub97c \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4. \ud558\ub098\uc758 \ubcf5\ub3c4\ub97c \ud1b5\uacfc\ud558\ub294 \ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc740 $1$\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubbfc\uaddc\ub294 $K$\uba85\uc758 \uce5c\uad6c\uc5d0\uac8c \ucef5\ub77c\uba74\uc744 \ub053\uc5ec\uc8fc\ub824\uace0 \ud55c\ub2e4. \ud604\uc7ac \ubbfc\uaddc\ub294 $1$\ubc88 \ubc29\uc5d0 \uc788\uc73c\uba70, \ubbfc\uaddc\ub97c \ud3ec\ud568\ud55c \ubaa8\ub4e0 \uce5c\uad6c\ub4e4\uc740 \uc11c\ub85c \ub2e4\ub978 \ubc29\uc5d0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub97c \uc704\ud574 \ubbfc\uaddc\ub294 \ubaa8\ub4e0 \uce5c\uad6c\ub4e4\uc5d0\uac8c \ub728\uac70\uc6b4 \ubb3c\uc744 \uc804\ub2ec\ud560 \uac83\uc774\ub2e4. \ub728\uac70\uc6b4 \ubb3c\uc740 \ubbfc\uaddc\uac00 \uc788\ub294 $1$\ubc88 \ubc29\uc758 \uc815\uc218\uae30\uc5d0\uc11c\ub9cc \uc5bb\uc744 \uc218 \uc788\ub2e4. \ub610\ud55c, \ubbfc\uaddc\ub294 \ub9e4\uc6b0 \ud070 \ubcf4\uc628\ubcd1\uc744 \uac00\uc9c0\uace0 \uc788\uc5b4 \ubb3c\uc744 \ud55c \ubc88\ub9cc \ubc1b\uc544\ub3c4 \ubaa8\ub4e0 \uce5c\uad6c\uc5d0\uac8c \uc904 \uc218 \uc788\ub294 \ucda9\ubd84\ud55c \uc591\uc758 \ubb3c\uc744 \ubc1b\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub77c\uba74\uc744 \ub053\uc774\ub294 \ud589\ub3d9\uc740 \uc704\ud5d8\ud55c \ud589\ub3d9\uc774\ub2e4. \uc0ac\uac10 \uc120\uc0dd\ub2d8\uaed8 \uac78\ub9ac\uba74 \ubc8c\uc810\uc744 \ubc1b\uc744 \uc218 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4. \ubbfc\uaddc\ub294 \uc704\ud5d8\uc744 \ucd5c\ub300\ud55c \uc904\uc774\uae30 \uc704\ud574 \uac00\uc7a5 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ub728\uac70\uc6b4 \ubb3c\uc744 \ubc30\ub2ec\ud55c \uc2dc\uac01\uc774 \ucd5c\ub300\ud55c \ube60\ub978 \ubc29\ubc95\uc73c\ub85c $K$\uac1c\uc758 \ubc29\uc744 \ubc29\ubb38\ud560 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubbfc\uaddc\uac00 $K$\uac1c\uc758 \ubc29\uc744 \ubc29\ubb38\ud558\ub294 \ubc29\ubc95\uc744 \ub354 \uc790\uc138\ud788 \uc124\uba85\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ubbfc\uaddc\ub294 \ubb3c\uc744 \ubc1b\uae30 \uc804, $K$\uba85\uc758 \uce5c\uad6c\ub4e4\uc774 \uc788\ub294 \ubc29\uc744 \ubbf8\ub9ac \ud655\uc778\ud55c\ub2e4.<\/li>\r\n\t<li>\ubbfc\uaddc\ub294 \uc2dc\uac01 $0$\uc5d0 $1$\ubc88 \ubc29\uc5d0\uc11c \ubb3c\uc744 \ubc1b\uace0 \ucd9c\ubc1c\ud574, \uac00\uc7a5 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ub728\uac70\uc6b4 \ubb3c\uc744 \ubc30\ub2ec\ud558\ub294 \uce5c\uad6c\uc5d0\uac8c \uac78\ub9ac\ub294 \uc2dc\uac04\uc744 \ucd5c\uc18c\ud654\ud558\ub294 \ubc29\ubc95\uc73c\ub85c $K$\uac1c\uc758 \ubc29\uc744 \ubc29\ubb38\ud560 \uac83\uc774\ub2e4.<\/li>\r\n\t<li>\uc2dc\uac04\uc744 \uacc4\uc0b0\ud560 \ub54c\ub294 \ubbfc\uaddc\uac00 \ubcf5\ub3c4\ub97c \uc774\ub3d9\ud558\ub294 \uc2dc\uac04\ub9cc \uace0\ub824\ud55c\ub2e4. \uce5c\uad6c\uc5d0\uac8c \ubb3c\uc744 \uc8fc\ub294 \uc2dc\uac04\uc774\ub098 \uc815\uc218\uae30\uc5d0\uc11c \ubb3c\uc744 \ub728\ub294 \uc2dc\uac04 \ub4f1\uc740 \ubb34\uc2dc\ud55c\ub2e4. <strong>\ubbfc\uaddc\uac00 \ubb3c\uc744 \ub2e4 \uc8fc\uace0 \uc790\uc2e0\uc758 \ubc29\uc73c\ub85c \ub3cc\uc544\uac00\ub294 \uc2dc\uac04 \uc5ed\uc2dc \ubb34\uc2dc\ud55c\ub2e4.<\/strong><\/li>\r\n<\/ul>\r\n\r\n<p>\ubbfc\uaddc\ub294 \uce5c\uad6c\ub4e4\uc774 \uc788\ub294 \ubc29\uc744 \ud655\uc778\ud558\uae30 \uc804\uc5d0, \uce5c\uad6c\ub4e4\uc5d0\uac8c \ubb3c\uc744 \ubc30\ub2ec\ud558\ub294 \ub370 \uc2dc\uac04\uc774 \uc5bc\ub9c8\ub098 \uac78\ub9b4\uc9c0 \uc608\uce21\ud558\ub824\uace0 \ud55c\ub2e4. $K$\uba85\uc758 \uce5c\uad6c\ub4e4\uc774 \uc788\ub294 \ubc29\uc744 \uace0\ub974\ub294 $\\binom{N-1}{K}$\uac00\uc9c0 \uacbd\uc6b0\uc5d0 \ub300\ud574, \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ubb3c\uc744 \ubc30\ub2ec\ud558\ub294 \uc2dc\uac01\uc758 \ud569\uc744 \uad6c\ud574 \uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubc29\uc758 \uc218 $N$\uacfc \uce5c\uad6c\uc758 \uc218 $K$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 $N$\ubc88\uc9f8 \uc904\uae4c\uc9c0 $i+1$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88 \ubcf5\ub3c4\uac00 \uc5f0\uacb0\ud558\ub294 \ub450 \ubc29\uc758 \ubc88\ud638 $U_i$\uc640 $V_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uce5c\uad6c\ub4e4\uc774 \uc788\ub294 \ubc29\uc744 \uace0\ub974\ub294 $\\binom{N-1}{K}$\uac00\uc9c0 \uacbd\uc6b0\uc5d0 \ub300\ud574 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ubb3c\uc744 \ubc30\ub2ec\ud558\ub294 \uc2dc\uac01\uc758 \ud569\uc744 $10^9 + 7$\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2\\le N\\le 10^5$<\/li>\r\n\t<li>$1\\le K\\le N-1$<\/li>\r\n\t<li>$1\\le U_i\\le N$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>$1\\le V_i\\le N$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>$U_i\\ne V_i$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \uc11c\uc6b8\uacfc\ud559\uace0\uc758 \uad6c\uc870\ub294 \ud2b8\ub9ac\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 10$<\/p>\r\n","subtask2":"<p>$N \\le 10^3$<\/p>\r\n","subtask3":"<p>\ucd94\uac00 \uc81c\ud55c \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"31070","problem_lang":"1","title":"Delivering Noodles","description":"<p>Seoul Science High School(SSHS) dormitory forms a tree with $N$ rooms connected with $N-1$ corridors. Every corridor can be passed in both directions, and it is possible to travel between all rooms. Traversing a corridor takes $1$ unit of time.<\/p>\r\n\r\n<p>Mingyu wants to prepare noodles for his $K$ friends. He is currently in room $1$, and he and his friends are all in distinct rooms.<\/p>\r\n\r\n<p>Mingyu will provide hot water for all his friends. He can only obtain hot water from the water purifier in his room (numbered $1$). Additionally, he has a big bottle, so he can deliver water to all his friends without needing to fill his bottle again.<\/p>\r\n\r\n<p>Preparing noodles is dangerous. If you get caught by the dormitory supervisor, you will get many demerit points. To reduce the risk of getting caught, he will visit the $K$ rooms so that the time of his last delivery is as early as possible.<\/p>\r\n\r\n<p>Precisely, he visits the $K$ rooms using the following method.<\/p>\r\n\r\n<ul>\r\n\t<li>Before filling his bottle with hot water, he obtains the information about the $K$ rooms where his friends are.<\/li>\r\n\t<li>After he fills his bottle from room $1$ in time $0$, he visits his $K$ friends in an order such that the last delivery is as early as possible.<\/li>\r\n\t<li>We only consider the time spent while walking through corridors. We ignore the time filling the bottle or delivering hot water to his friends. <strong>We also ignore the time Mingyu returns to his room after his last delivery.<\/strong><\/li>\r\n<\/ul>\r\n\r\n<p>Before checking what $K$ rooms his friends are in, Mingyu wants to predict how long it will take to deliver water to all his friends. Please calculate the sum of the earliest possible time of the last delivery for all $\\binom{N-1}{K}$ different ways his friends can be in their rooms.<\/p>\r\n","input":"<p>The first line contains two integers $N$ and $K$ &mdash; the number of rooms and the number of friends, respectively. They are separated by a space.<\/p>\r\n\r\n<p>From the second line to $N$-th line, the $i+1$-th line contains two integers $U_i$ and $V_i$ &mdash; the rooms&rsquo; index which the $i$-th corridor connects.<\/p>\r\n","output":"<p>In the first line, print the sum of the time of the last delivery for all $\\binom{N-1}{K}$ different ways in which his friends can be in their rooms, modulo $10^9 + 7$.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2\\le N\\le 10^5$<\/li>\r\n\t<li>$1\\le K\\le N-1$<\/li>\r\n\t<li>$1\\le U_i\\le N$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>$1\\le V_i\\le N$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>$U_i\\ne V_i$ $(1\\le i&lt;N)$<\/li>\r\n\t<li>The structure of SSHS dormitory in the input forms a valid tree.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 10$<\/p>\r\n","subtask2":"<p>$N \\le 10^3$<\/p>\r\n","subtask3":"<p>There are no additional constraints.<\/p>\r\n"}]