시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 17 3 3 18.750%

문제

"나이트"는 한국에서 엄청나게 유행하는 새 게임이다. 강산이와 창영이는 대세에 뒤쳐지지 않기 위해서 이 게임을 플레이하려고 한다. 강산이는 체스에서 사용하는 나이트 말을 N*N 체스판 위에 놓는다. 그 다음에, 창영이는 눈가리개를 하고, 강산이는 1초에 한 번씩 나이트를 T번 움직인다. 이렇게 움직인 이후에, 창영이가 나이트의 최종 위치를 맞추면 이기는 게임이다.

이 게임에서 사용하는 체스판은 보통 체스판이 아니다. 각 칸에는 숫자가 하나씩 써있다. 어떤 칸에 쓰여 있는 수를 K라고 한다면, 시작한지 0, K, 2K, 3k, ...초 이었을 때만 나이트가 이동할 수 있는 칸이다. 

게임은 0초일 때 시작된다. 강산이는 나이트를 움직일 수 있는 8개 칸 중 한 칸으로 반드시 이동시켜야 한다. 나이트가 그 자리에 있는 시간 동안 (i초 일 때, 나이트르 움직였다면 i+1초) 그 칸은 나이트가 이동할 수 있는 칸이어야 한다.

창영이를 도와서 T번 움직인 이후에 나이트가 있을 수 있는 곳의 위치를 모두 구하는 프로그램을 작성하시오.

입력

첫째 줄에 체스판의 크기 N과 강산이가 나이트를 움직이는 횟수 T가 주어진다. (3 ≤ N ≤ 30, 1 ≤ T ≤ 1,000,000)

둘째 줄에는 나이트의 시작 위치 X와 Y가 주어진다. (1 ≤ X, Y ≤ N)

다음 N개 줄에는 체스판에 쓰여 있는 숫자가 주어진다. 이 값은 109보다 작거나 같은 자연수이다.

출력

첫째 줄에 T번 움직인 이후에 나이트가 있을 수 있는 곳의 위치의 수 M을 출력한다.

다음 M개 줄에는 그 위치를 한 줄에 하나씩 행이 증가하는 순서로, 행이 같다면 열이 증가하는 순서로 출력한다.

예제 입력 1

3 2
1 1
1 3 2
2 3 2
3 1 1

예제 출력 1

2
1 1
1 3

힌트

[{"problem_id":"2833","problem_lang":"0","title":"\ub098\uc774\ud2b8","description":"<p>&quot;\ub098\uc774\ud2b8&quot;\ub294 \ud55c\uad6d\uc5d0\uc11c \uc5c4\uccad\ub098\uac8c \uc720\ud589\ud558\ub294 \uc0c8 \uac8c\uc784\uc774\ub2e4. \uac15\uc0b0\uc774\uc640 \ucc3d\uc601\uc774\ub294 \ub300\uc138\uc5d0 \ub4a4\uccd0\uc9c0\uc9c0 \uc54a\uae30 \uc704\ud574\uc11c \uc774 \uac8c\uc784\uc744 \ud50c\ub808\uc774\ud558\ub824\uace0 \ud55c\ub2e4. \uac15\uc0b0\uc774\ub294 \uccb4\uc2a4\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \ub098\uc774\ud2b8 \ub9d0\uc744 N*N \uccb4\uc2a4\ud310 \uc704\uc5d0 \ub193\ub294\ub2e4. \uadf8 \ub2e4\uc74c\uc5d0, \ucc3d\uc601\uc774\ub294 \ub208\uac00\ub9ac\uac1c\ub97c \ud558\uace0, \uac15\uc0b0\uc774\ub294 1\ucd08\uc5d0 \ud55c \ubc88\uc529 \ub098\uc774\ud2b8\ub97c T\ubc88 \uc6c0\uc9c1\uc778\ub2e4. \uc774\ub807\uac8c \uc6c0\uc9c1\uc778 \uc774\ud6c4\uc5d0, \ucc3d\uc601\uc774\uac00 \ub098\uc774\ud2b8\uc758 \ucd5c\uc885 \uc704\uce58\ub97c \ub9de\ucd94\uba74 \uc774\uae30\ub294 \uac8c\uc784\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uac8c\uc784\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uccb4\uc2a4\ud310\uc740 \ubcf4\ud1b5 \uccb4\uc2a4\ud310\uc774 \uc544\ub2c8\ub2e4. \uac01 \uce78\uc5d0\ub294 \uc22b\uc790\uac00 \ud558\ub098\uc529 \uc368\uc788\ub2e4. \uc5b4\ub5a4 \uce78\uc5d0 \uc4f0\uc5ec \uc788\ub294 \uc218\ub97c K\ub77c\uace0 \ud55c\ub2e4\uba74, \uc2dc\uc791\ud55c\uc9c0 0, K, 2K, 3k, ...\ucd08 \uc774\uc5c8\uc744 \ub54c\ub9cc \ub098\uc774\ud2b8\uac00 \uc774\ub3d9\ud560 \uc218 \uc788\ub294 \uce78\uc774\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 0\ucd08\uc77c \ub54c \uc2dc\uc791\ub41c\ub2e4. \uac15\uc0b0\uc774\ub294 \ub098\uc774\ud2b8\ub97c \uc6c0\uc9c1\uc77c \uc218 \uc788\ub294 8\uac1c \uce78 \uc911 \ud55c \uce78\uc73c\ub85c \ubc18\ub4dc\uc2dc \uc774\ub3d9\uc2dc\ucf1c\uc57c \ud55c\ub2e4. \ub098\uc774\ud2b8\uac00 \uadf8 \uc790\ub9ac\uc5d0 \uc788\ub294 \uc2dc\uac04 \ub3d9\uc548 (i\ucd08 \uc77c \ub54c, \ub098\uc774\ud2b8\ub974 \uc6c0\uc9c1\uc600\ub2e4\uba74 i+1\ucd08) \uadf8 \uce78\uc740 \ub098\uc774\ud2b8\uac00 \uc774\ub3d9\ud560 \uc218 \uc788\ub294 \uce78\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ucc3d\uc601\uc774\ub97c \ub3c4\uc640\uc11c T\ubc88 \uc6c0\uc9c1\uc778 \uc774\ud6c4\uc5d0 \ub098\uc774\ud2b8\uac00 \uc788\uc744 \uc218 \uc788\ub294 \uacf3\uc758 \uc704\uce58\ub97c \ubaa8\ub450 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uccb4\uc2a4\ud310\uc758 \ud06c\uae30 N\uacfc \uac15\uc0b0\uc774\uac00 \ub098\uc774\ud2b8\ub97c \uc6c0\uc9c1\uc774\ub294 \ud69f\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N &le; 30, 1 &le; T &le; 1,000,000)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 \ub098\uc774\ud2b8\uc758 \uc2dc\uc791 \uc704\uce58 X\uc640 Y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; X, Y &le; N)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uccb4\uc2a4\ud310\uc5d0 \uc4f0\uc5ec \uc788\ub294 \uc22b\uc790\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uac12\uc740 10<sup>9<\/sup>\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 T\ubc88 \uc6c0\uc9c1\uc778 \uc774\ud6c4\uc5d0 \ub098\uc774\ud2b8\uac00 \uc788\uc744 \uc218 \uc788\ub294 \uacf3\uc758 \uc704\uce58\uc758 \uc218 M\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uadf8 \uc704\uce58\ub97c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ud589\uc774 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c, \ud589\uc774 \uac19\ub2e4\uba74 \uc5f4\uc774 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/chessmania.png\" style=\"height:203px; width:557px\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2833","problem_lang":"1","title":"SKAKAC","description":"<p>Mirko and Slavko are playing the popular new game known as The Knight. Mirko places a knight chess piece on an NxN chessboard and, with Slavko blindfolded, makes exactly T moves, one per second. After that, Slavko must guess the final position of the knight in order to win.&nbsp;<\/p>\r\n\r\n<p>The chessboard in this game is unusual in that each square is blocked part of the time. More precisely, each square is labelled by a positive integer. A square labelled by number K is clear only during seconds 0, K, 2K, 3K etc; it is blocked at all other times. The knight can, of course, occupy a square only while the square is clear.&nbsp;<\/p>\r\n\r\n<p>The game begins in second 0. In each second Mirko must make a move (selecting one of 8 possible Lshaped moves, two squares in one direction and one square in the other, as per standard chess rules), provided that the destination square is not blocked during the next second. Help Slavko by writing a program to calculate all possible squares that the knight can possibly occupy after T moves.<\/p>\r\n","input":"<p>The first line of input contains two positive integers, N (3 &le; N &le; 30), the size of the chessboard, and T (1 &le; T &le; 1 000 000), the number of moves that Mirko will make.<\/p>\r\n\r\n<p>The second line of input contains two positive integers X and Y (1 &le; X, Y &le; N), the row and column indices of the knight&rsquo;s starting square selected by Mirko.&nbsp;<\/p>\r\n\r\n<p>The next N lines each contain N positive integers less than 10<sup>9<\/sup> (one billion), the values of K for the corresponding chessboard squares.&nbsp;<\/p>\r\n","output":"<p>The first line of output must contain the nonnegative integer M, the number of squares that the knight can possibly occupy after T moves.&nbsp;<\/p>\r\n\r\n<p>The next M lines must contain indices of those squares, sorted by increasing row index, with cells in the same row sorted by increasing column index.&nbsp;<\/p>\r\n","hint":"<p>The state of the chessboard in each second is shown below. Clear cells are denoted by &lsquo;.&rsquo;, blocked cells by &lsquo;#&rsquo;, and possible locations of the knight by &lsquo;K&rsquo;.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/chessmania.png\" style=\"height:203px; width:557px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]