문제
레이저박스라는 게임은 정사각형 모양의 n x n 보드에서 진행한다. (체스판을 상상하면 된다) 레이저박스의 임의의 칸마다 우향우 거울이라는 장치가 설치되어 있고, 마지막으로 레이저 한개가 설치되어 있다. 레이저는 판의 끝에만 설치 될 수 있는데, 행의 맨 아래/맨 위, 열의 오른쪽 끝/왼쪽 끝에 설치 될 수 있다. 레이저에서 나온 빔은 그 행 혹은 열을 질러서 반대쪽을 비춘다.
게임은 우향우 거울을 임의의 칸마다 설치한 후, 레이저를 배치를 해 놓은 이후에 시작한다. 레이저를 켰을 때 나온 빔이 우향우 거울을 통과하면 진입한 방향과는 관계 없이 오른쪽으로 90도를 꺾어 다시 나아간다.
레이저 빔이 마지막으로 어느 좌표를 향해 비춰지는지 구하라.
출력
매 테스트케이스마다 빔이 보드를 떠나는 좌표 X Y를 출력하라. 레이저의 좌표와 마찬가지로 빔은 보드 밖으로 떠나기에 좌표에는 0 혹은 n + 1이 포함된다.
만약 빔이 보드 밖을 떠나지 않을 경우의 출력은 0 0이 된다.
[{"problem_id":"3709","problem_lang":"0","title":"\ub808\uc774\uc800\ube54\uc740 \uc5b4\ub514\ub85c","description":"<p>\ub808\uc774\uc800\ubc15\uc2a4\ub77c\ub294 \uac8c\uc784\uc740 \uc815\uc0ac\uac01\ud615 &nbsp;\ubaa8\uc591\uc758 n x n \ubcf4\ub4dc\uc5d0\uc11c \uc9c4\ud589\ud55c\ub2e4. (\uccb4\uc2a4\ud310\uc744 \uc0c1\uc0c1\ud558\uba74 \ub41c\ub2e4) \ub808\uc774\uc800\ubc15\uc2a4\uc758 \uc784\uc758\uc758 \uce78\ub9c8\ub2e4 \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc774\ub77c\ub294 \uc7a5\uce58\uac00 \uc124\uce58\ub418\uc5b4 \uc788\uace0, \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ub808\uc774\uc800 \ud55c\uac1c\uac00 \uc124\uce58\ub418\uc5b4 \uc788\ub2e4. \ub808\uc774\uc800\ub294 \ud310\uc758 \ub05d\uc5d0\ub9cc \uc124\uce58 \ub420 \uc218 \uc788\ub294\ub370, \ud589\uc758 \ub9e8 \uc544\ub798\/\ub9e8 \uc704, \uc5f4\uc758 \uc624\ub978\ucabd \ub05d\/\uc67c\ucabd \ub05d\uc5d0 \uc124\uce58 \ub420 \uc218 \uc788\ub2e4. \ub808\uc774\uc800\uc5d0\uc11c \ub098\uc628 \ube54\uc740 \uadf8 \ud589 \ud639\uc740 \uc5f4\uc744 \uc9c8\ub7ec\uc11c \ubc18\ub300\ucabd\uc744 \ube44\ucd98\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc744 \uc784\uc758\uc758 \uce78\ub9c8\ub2e4 \uc124\uce58\ud55c \ud6c4, \ub808\uc774\uc800\ub97c \ubc30\uce58\ub97c \ud574 \ub193\uc740 \uc774\ud6c4\uc5d0 \uc2dc\uc791\ud55c\ub2e4. \ub808\uc774\uc800\ub97c \ucf30\uc744 \ub54c \ub098\uc628 \ube54\uc774 \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc744 \ud1b5\uacfc\ud558\uba74 \uc9c4\uc785\ud55c \ubc29\ud5a5\uacfc\ub294 \uad00\uacc4 \uc5c6\uc774 \uc624\ub978\ucabd\uc73c\ub85c 90\ub3c4\ub97c \uaebe\uc5b4 \ub2e4\uc2dc \ub098\uc544\uac04\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ub808\uc774\uc800 \ube54\uc774 \ub9c8\uc9c0\ub9c9\uc73c\ub85c \uc5b4\ub290 \uc88c\ud45c\ub97c \ud5a5\ud574 \ube44\ucdb0\uc9c0\ub294\uc9c0 \uad6c\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \ucd1d \uac1c\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d0\ub294 \ubcf4\ub4dc\uc758 \ud06c\uae30 n(1 &le; n &le; 50)\uacfc \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc758 \uac1c\uc218 r(1 &le; r &le; 50)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4\uc9c0\ub294 r\uac1c\uc758 \uc904\uc5d0\ub294 \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc774 \ubc30\uce58\ub41c \uc88c\ud45c x y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.(\uc88c\ud45c\ub294 1\ubd80\ud130 \uc2dc\uc791\ud55c\ub2e4) \uc911\ubcf5\ub41c \uc88c\ud45c\ub294 \uc788\uc744 \uc218 \uc5c6\uace0, \ub9e4 \uce78\ub9c8\ub2e4 \ucd5c\ub300 1\uac1c\uc758 \uc6b0\ud5a5\uc6b0 \uac70\uc6b8\uc774 \ub193\uc77c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 \ub808\uc774\uc800\uc758 \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub808\uc774\uc800\ub294 \ud589\uacfc \uc5f4\uc758 \ub05d, \uc989 \ud310 \ubc16\uc5d0 \uc704\uce58\ud574\uc57c \ud558\ubbc0\ub85c \ub808\uc774\uc800\uc758 \uc88c\ud45c\uc5d0\ub294 0 \ud639\uc740 n + 1\uc774 \ud3ec\ud568\ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, 2x2\ubcf4\ub4dc\uc758 1\ud589 \ub9e8 \ubc11\uc5d0\uc11c \uc704\ub85c \uc3d8\uc544\uc9c0\ub294 \ub808\uc774\uc800\uc758 \uc88c\ud45c\ub294 (3, 1)\ub85c\uc368 \uc8fc\uc5b4\uc9c4\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c 6x6\ubcf4\ub4dc\uc758 6\uc5f4 \uc67c\ucabd \ub05d\uc5d0\uc11c \uc624\ub978\ucabd \ub05d\uc73c\ub85c \uc3d8\uc544\uc9c0\ub294 \ub808\uc774\uc800\uc758 \uc88c\ud45c\ub294 (6, 0)\uc774 \ub418\uaca0\ub2e4.<\/p>\r\n","output":"<p>\ub9e4 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\ub9c8\ub2e4 \ube54\uc774 \ubcf4\ub4dc\ub97c \ub5a0\ub098\ub294 \uc88c\ud45c X Y\ub97c \ucd9c\ub825\ud558\ub77c. \ub808\uc774\uc800\uc758 \uc88c\ud45c\uc640 \ub9c8\ucc2c\uac00\uc9c0\ub85c \ube54\uc740 \ubcf4\ub4dc \ubc16\uc73c\ub85c \ub5a0\ub098\uae30\uc5d0 \uc88c\ud45c\uc5d0\ub294 0 \ud639\uc740 n + 1\uc774 \ud3ec\ud568\ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ub9cc\uc57d \ube54\uc774 \ubcf4\ub4dc \ubc16\uc744 \ub5a0\ub098\uc9c0 \uc54a\uc744 \uacbd\uc6b0\uc758 \ucd9c\ub825\uc740 0 0\uc774 \ub41c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3709","problem_lang":"1","title":"Laserbox","description":"<p>A laserbox is a game involving some optical equipment. The game board is a square n &times; n grid. On each grid point, a gadget called a right-turner can be placed and several such gadgets are included. Finally, there is a ruby laser, and if the laser is mounted at the bottom end of a column, the beam will be directed northwards through that column. Analogously, the laser beam may be directed southwards from the top of a column, eastwards from the start of a row or westwards from the end of the row.<\/p>\r\n\r\n<p>The game starts with some right-turners being spread out on some grid points and the laser (switched off) being mounted somewhere along the border of the rectangle. The player then tries to deduce where the beam will emerge when the laser is switched on. The effect of a right-turner is to deflect the beam ninety degrees to the right, regardless of from which of the four directions it enters.<\/p>\r\n\r\n<p>Your program must do exactly what the player is supposed to do.<\/p>\r\n","input":"<p>On the first line of the input is a single positive integer, telling the number of test cases to follow. The first line of each test case consists of two integers n r, where 1 &le; n &le; 50 is the size of the board and 1 &le; r &le; 50 the number of right-turners. The following r lines contain the coordinates x y of the right-turners. No two right-turners will have the same coordinates.<\/p>\r\n\r\n<p>Finally, a line with two integers indicating the laser position follows. The bottom of column six is denoted by 6 0 and the start of row seven by 0 7. If the zeroes are replaced by n + 1, the laser is placed at the top of column six and the end of row seven, respectively<\/p>\r\n","output":"<p>For each test case, output one line containing the coordinates X Y of the beam as it leaves the board. The same rules as for the laser apply, so X may equal 0 or n + 1 or else Y equal 0 or n + 1. If the beam gets caught and does not leave the board, the output should be 0 0.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]
