시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 19 10 10 71.429%

문제

영수는 가로 N, 세로 M 크기의 판 위에, 각 변의 길이가 1인 정육면체 블록을 쌓는 놀이를 하고 있었다. 그러다가 중간에 잠시 중지할 일이 생겼는데, 나중에 계속 블록을 쌓기 위해 쌓아놓은 블록들을 앞면과 옆면에서 본 모습을 그려 두었다. 예를 들어 다음과 같은 예를 보자.

왼쪽은 앞에서 본 모습이고, 오른쪽은 옆에서 본 모습이다. 영수는 나중에 블록을 원래의 모습으로 복원하려고 했는데, 복원을 하다 보니 예전에 그려둔 그림만으로는 원래의 모습이 유일하게 결정되지 않음을 알게 되었다. 그래서 영수는 두 가지 경우를 생각해 보기로 했는데, 하나는 블록의 개수가 최대가 되는 경우이고, 다른 하나는 블록의 개수가 최소가 되는 경우이다.

왼쪽은 위의 그림을 바탕으로 블록의 개수가 최대가 되도록 쌓은 경우고, 가운데는 최소가 되도록 쌓은 모습이다. 오른쪽 그림은 최소가 될 때의 모습을 뒤에서 본 것이다. 최대는 21개의 블록이 필요하고, 최소는 10개의 블록이 필요하다.

입력

첫째 줄에 두 정수 N, M(1≤N, M≤100,000)이 주어진다. 다음 줄에는 N개의 정수로, 쌓아 놓은 블록을 앞에서 보았을 때의 모습이 주어진다. 이는 왼쪽부터 차례로 높이를 나타낸다. 같은 방식으로 다음 줄에 M개의 정수로 각각의 높이가 주어진다. 각각의 높이는 int 범위(약 10^9)를 넘지 않는다.

출력

첫째 줄에 최소 블록, 최대 블록을 출력한다. 답은 int 범위를 넘지 않으며, 만약 불가능한 경우가 주어지면 -1을 출력한다.

예제 입력 1

4 3
1 3 4 2
1 4 2

예제 출력 1

10 21
[{"problem_id":"2388","problem_lang":"0","title":"\ube14\ub85d \uc313\uae30","description":"<p>\uc601\uc218\ub294 \uac00\ub85c N, \uc138\ub85c M \ud06c\uae30\uc758 \ud310 \uc704\uc5d0, \uac01 \ubcc0\uc758 \uae38\uc774\uac00 1\uc778 \uc815\uc721\uba74\uccb4 \ube14\ub85d\uc744 \uc313\ub294 \ub180\uc774\ub97c \ud558\uace0 \uc788\uc5c8\ub2e4. \uadf8\ub7ec\ub2e4\uac00 \uc911\uac04\uc5d0 \uc7a0\uc2dc \uc911\uc9c0\ud560 \uc77c\uc774 \uc0dd\uacbc\ub294\ub370, \ub098\uc911\uc5d0 \uacc4\uc18d \ube14\ub85d\uc744 \uc313\uae30 \uc704\ud574 \uc313\uc544\ub193\uc740 \ube14\ub85d\ub4e4\uc744 \uc55e\uba74\uacfc \uc606\uba74\uc5d0\uc11c \ubcf8 \ubaa8\uc2b5\uc744 \uadf8\ub824 \ub450\uc5c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \ub2e4\uc74c\uacfc \uac19\uc740 \uc608\ub97c \ubcf4\uc790.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201103\/BIN0001(1).png\" style=\"height:105px; width:218px\" \/><\/p>\r\n\r\n<p>\uc67c\ucabd\uc740 \uc55e\uc5d0\uc11c \ubcf8 \ubaa8\uc2b5\uc774\uace0, \uc624\ub978\ucabd\uc740 \uc606\uc5d0\uc11c \ubcf8 \ubaa8\uc2b5\uc774\ub2e4. \uc601\uc218\ub294 \ub098\uc911\uc5d0 \ube14\ub85d\uc744 \uc6d0\ub798\uc758 \ubaa8\uc2b5\uc73c\ub85c \ubcf5\uc6d0\ud558\ub824\uace0 \ud588\ub294\ub370, \ubcf5\uc6d0\uc744 \ud558\ub2e4 \ubcf4\ub2c8 \uc608\uc804\uc5d0 \uadf8\ub824\ub454 \uadf8\ub9bc\ub9cc\uc73c\ub85c\ub294 \uc6d0\ub798\uc758 \ubaa8\uc2b5\uc774 \uc720\uc77c\ud558\uac8c \uacb0\uc815\ub418\uc9c0 \uc54a\uc74c\uc744 \uc54c\uac8c \ub418\uc5c8\ub2e4. \uadf8\ub798\uc11c \uc601\uc218\ub294 \ub450 \uac00\uc9c0 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud574 \ubcf4\uae30\ub85c \ud588\ub294\ub370, \ud558\ub098\ub294 \ube14\ub85d\uc758 \uac1c\uc218\uac00 \ucd5c\ub300\uac00 \ub418\ub294 \uacbd\uc6b0\uc774\uace0, \ub2e4\ub978 \ud558\ub098\ub294 \ube14\ub85d\uc758 \uac1c\uc218\uac00 \ucd5c\uc18c\uac00 \ub418\ub294 \uacbd\uc6b0\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201103\/BIN0002(1).png\" style=\"height:129px; width:466px\" \/><\/p>\r\n\r\n<p>\uc67c\ucabd\uc740 \uc704\uc758 \uadf8\ub9bc\uc744 \ubc14\ud0d5\uc73c\ub85c \ube14\ub85d\uc758 \uac1c\uc218\uac00 \ucd5c\ub300\uac00 \ub418\ub3c4\ub85d \uc313\uc740 \uacbd\uc6b0\uace0, \uac00\uc6b4\ub370\ub294 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \uc313\uc740 \ubaa8\uc2b5\uc774\ub2e4. \uc624\ub978\ucabd \uadf8\ub9bc\uc740 \ucd5c\uc18c\uac00 \ub420 \ub54c\uc758 \ubaa8\uc2b5\uc744 \ub4a4\uc5d0\uc11c \ubcf8 \uac83\uc774\ub2e4. \ucd5c\ub300\ub294 21\uac1c\uc758 \ube14\ub85d\uc774 \ud544\uc694\ud558\uace0, \ucd5c\uc18c\ub294 10\uac1c\uc758 \ube14\ub85d\uc774 \ud544\uc694\ud558\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 N, M(1&le;N, M&le;100,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 N\uac1c\uc758 \uc815\uc218\ub85c, \uc313\uc544 \ub193\uc740 \ube14\ub85d\uc744 \uc55e\uc5d0\uc11c \ubcf4\uc558\uc744 \ub54c\uc758 \ubaa8\uc2b5\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uc67c\ucabd\ubd80\ud130 \ucc28\ub840\ub85c \ub192\uc774\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \ub2e4\uc74c \uc904\uc5d0 M\uac1c\uc758 \uc815\uc218\ub85c \uac01\uac01\uc758 \ub192\uc774\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01\uac01\uc758 \ub192\uc774\ub294 int \ubc94\uc704(\uc57d 10^9)\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ucd5c\uc18c \ube14\ub85d, \ucd5c\ub300 \ube14\ub85d\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub2f5\uc740 int \ubc94\uc704\ub97c \ub118\uc9c0 \uc54a\uc73c\uba70, \ub9cc\uc57d \ubd88\uac00\ub2a5\ud55c \uacbd\uc6b0\uac00 \uc8fc\uc5b4\uc9c0\uba74 -1\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2388","problem_lang":"1","title":"Block Town","description":"<p>Children like playing with blocks (cube wooden bricks). They usually build high towers, but small Johny dreams of different plans. He is going to build a big town. His daddy has bought him a rectangular table; its width is K blocks and its length is L blocks exactly. Johny decided to project a plan of such a town before he starts building the town itself. He has drawn a square-shaped network on the table consisting of KxL squares. He wants to place the towers consisting of one or more blocks on some of the squares of the network drawn; the remaining squares will be empty. Because of the table being so large, Johny is not going to plan exactly for every square how many blocks he will put on it. He only wants to decide about front and right sight shapes of his town. He drew these two views (two-dimensional projections of the planned town) on a paper. You can see an example of these drawings and the adequate town made of wooden bricks in the pictures:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/blocktown.png\" style=\"height:165px; width:662px\" \/><\/p>\r\n\r\n<p>Johny&#39;s daddy is afraid they don&#39;t have enough blocks to finish building Johny&#39;s planned town. You are asked for writing a program to compute the minimal and maximal amount of blocks with which a town corresponding to Johny&#39;s plans can be built. Moreover the program can decide about the possibility of building a town satisfying the views.<\/p>\r\n","input":"<p>The first line of input file TOWN.IN contains two positive integers K, L -- the width and the length of the table (expressed as numbers of bricks). Neither the width nor the length of the table is greater than 100000 bricks. The following lines of the input file contain the description of the front view of the town. The description consists of a series of heights of visible buildings on each square from the left to the right (the height is measured by the number of the blocks, too). There is only one number on each line, i.e. the number of the lines with the front view description of the town equals K -- the width of the table. Similarly the next L lines of the input file contain the right sight view of the town. The heights of the wooden block towers are now specified from the front line to the back line. You may suppose there is no building in the town with height exceeding 5000 blocks. The maximal number of blocks needed for building the entire town does not exceed 2000000000.<\/p>\r\n","output":"<p>Output file TOWN.OUT contains only one line. If it is not possible to build a town with the front and right sight views given, only a text `No solution.&#39; is written there. In the other case two numbers will be written on the line and separated by a single space. The first one is the minimal and the second one is the maximal amount of blocks small Johny can use to build his town in accordance with his project.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]