문제
이 문제는 1차원 돌 게임 1 과 굵은 글씨로 적힌 부분만 다릅니다.
동우와 재우는 1ドル\times n$ 모양의 직선형 격자판에서 처음에 한 칸에 한 개씩 돌을 올려 둔 상태로 게임을 진행하려 한다.
게임은 동우부터 시작해 턴을 번갈아 가면서 돌을 가져간다. 즉, 동우는 홀수 번째 턴에, 재우는 짝수 번째 턴에 진행한다.
첫 번째 턴에는 1ドル$개의 칸을 골라 그곳에 놓인 돌을 가져간다.
두 번째 턴부터는 직전 턴에 상대방이 가져간 돌의 개수가 $x$개라면, 1ドル$ 이상 $x+1$ 이하의 정수 $y$를 하나 골라서, 돌이 놓여져 있는 연속한 $y$개의 칸을 골라 그 영역에 놓인 모든 돌을 가져간다.
돌을 가져갈 때마다, 돌을 가져간 칸(들)을 기준으로 남은 돌들이 두 부분으로 나누어진다면, 놓인 돌의 개수가 더 적은 부분에 놓인 돌을 모두 버린다. 두 부분에 놓인 돌의 개수가 같다면 한 부분을 선택해 놓인 돌을 모두 버린다. 두 부분으로 나누어지지 않고 한 부분만 있는 경우 버리지 않는다.
자신의 턴에 조건에 맞게 돌을 가져가지 못한다면 그 사람이 패배하며, 상대방이 승리한다.
둘 다 승리하기 위해 최선의 플레이를 한다면 누가 이기는지 출력하시오.
출력
각 테스트 케이스에 대해 동우가 이기면 kidw0124eoaud0108
서브태스크 번호 배점 제한 1 28 $n\le 20$
2 34 $n\le 1,000円$
3 133 $n\le 500,000円$
4 155 추가적인 제한 조건 없음
예제 출력 1
복사
kidw0124
kidw0124
eoaud0108
$n=4$인 경우 동우는 첫 번째 턴에 가장 마지막(4ドル$번째) 칸에 놓인 돌을 가져가면 승리할 수 있다.
두 번째 턴에 재우는 남은 3ドル$칸에 놓인 돌들 중 이웃한 1ドル$개 혹은 2ドル$개를 골라 가져가는데, 다음과 같은 경우가 가능하다. 좌우 대칭인 상황은 하나만 생각하자.
1ドル$ 혹은 3ドル$번 칸에 놓인 돌을 가져갈 경우
1ドル,ドル 2ドル$번 혹은 2ドル,ドル 3ドル$번 칸에 놓인 돌을 가져갈 경우
모든 경우에 대해 동우는 남은 돌을 가져갈 수 있으며, 재우는 네 번째 턴을 진행할 수 없다.
[{"problem_id":"31542","problem_lang":"0","title":"1\ucc28\uc6d0 \ub3cc \uac8c\uc784 2","description":"<blockquote>\r\n<p>\uc774 \ubb38\uc81c\ub294 <a href=\"\/problem\/31541\">1\ucc28\uc6d0 \ub3cc \uac8c\uc784 1<\/a>\uacfc <strong>\uad75\uc740<\/strong> \uae00\uc528\ub85c \uc801\ud78c \ubd80\ubd84\ub9cc \ub2e4\ub985\ub2c8\ub2e4.<\/p>\r\n<\/blockquote>\r\n\r\n<p>\ub3d9\uc6b0\uc640 \uc7ac\uc6b0\ub294 $1\\times n$ \ubaa8\uc591\uc758 \uc9c1\uc120\ud615 \uaca9\uc790\ud310\uc5d0\uc11c \ucc98\uc74c\uc5d0 \ud55c \uce78\uc5d0 \ud55c \uac1c\uc529 \ub3cc\uc744 \uc62c\ub824 \ub454 \uc0c1\ud0dc\ub85c \uac8c\uc784\uc744 \uc9c4\ud589\ud558\ub824 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 \ub3d9\uc6b0\ubd80\ud130 \uc2dc\uc791\ud574 \ud134\uc744 \ubc88\uac08\uc544 \uac00\uba74\uc11c \ub3cc\uc744 \uac00\uc838\uac04\ub2e4. \uc989, \ub3d9\uc6b0\ub294 \ud640\uc218 \ubc88\uc9f8 \ud134\uc5d0, \uc7ac\uc6b0\ub294 \uc9dd\uc218 \ubc88\uc9f8 \ud134\uc5d0 \uc9c4\ud589\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab \ubc88\uc9f8 \ud134\uc5d0\ub294 $1$\uac1c\uc758 \uce78\uc744 \uace8\ub77c \uadf8\uacf3\uc5d0 \ub193\uc778 \ub3cc\uc744 \uac00\uc838\uac04\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \ud134\ubd80\ud130\ub294 \uc9c1\uc804 \ud134\uc5d0 \uc0c1\ub300\ubc29\uc774 \uac00\uc838\uac04 \ub3cc\uc758 \uac1c\uc218\uac00 $x$\uac1c\ub77c\uba74, <strong>$1$ \uc774\uc0c1 $x+1$ \uc774\ud558\uc758 \uc815\uc218 $y$\ub97c \ud558\ub098 \uace8\ub77c\uc11c, \ub3cc\uc774 \ub193\uc5ec\uc838 \uc788\ub294 \uc5f0\uc18d\ud55c $y$\uac1c\uc758 \uce78\uc744 \uace8\ub77c<\/strong> \uadf8 \uc601\uc5ed\uc5d0 \ub193\uc778 \ubaa8\ub4e0 \ub3cc\uc744 \uac00\uc838\uac04\ub2e4.<\/li>\r\n\t<li>\ub3cc\uc744 \uac00\uc838\uac08 \ub54c\ub9c8\ub2e4, \ub3cc\uc744 \uac00\uc838\uac04 \uce78(\ub4e4)\uc744 \uae30\uc900\uc73c\ub85c \ub0a8\uc740 \ub3cc\ub4e4\uc774 \ub450 \ubd80\ubd84\uc73c\ub85c \ub098\ub204\uc5b4\uc9c4\ub2e4\uba74, \ub193\uc778 \ub3cc\uc758 \uac1c\uc218\uac00 \ub354 \uc801\uc740 \ubd80\ubd84\uc5d0 \ub193\uc778 \ub3cc\uc744 \ubaa8\ub450 \ubc84\ub9b0\ub2e4. \ub450 \ubd80\ubd84\uc5d0 \ub193\uc778 \ub3cc\uc758 \uac1c\uc218\uac00 \uac19\ub2e4\uba74 \ud55c \ubd80\ubd84\uc744 \uc120\ud0dd\ud574 \ub193\uc778 \ub3cc\uc744 \ubaa8\ub450 \ubc84\ub9b0\ub2e4. \ub450 \ubd80\ubd84\uc73c\ub85c \ub098\ub204\uc5b4\uc9c0\uc9c0 \uc54a\uace0 \ud55c \ubd80\ubd84\ub9cc \uc788\ub294 \uacbd\uc6b0 \ubc84\ub9ac\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n\t<li>\uc790\uc2e0\uc758 \ud134\uc5d0 \uc870\uac74\uc5d0 \ub9de\uac8c \ub3cc\uc744 \uac00\uc838\uac00\uc9c0 \ubabb\ud55c\ub2e4\uba74 \uadf8 \uc0ac\ub78c\uc774 \ud328\ubc30\ud558\uba70, \uc0c1\ub300\ubc29\uc774 \uc2b9\ub9ac\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub458 \ub2e4 \uc2b9\ub9ac\ud558\uae30 \uc704\ud574 \ucd5c\uc120\uc758 \ud50c\ub808\uc774\ub97c \ud55c\ub2e4\uba74 \ub204\uac00 \uc774\uae30\ub294\uc9c0 \ucd9c\ub825\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 $T$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $(1\\le T \\le 10^6)$<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ubcc4\ub85c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd08\uae30\uc758 \ub3cc\uc758 \uac1c\uc218 $n$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. $(1\\le n\\le 10^{18})$<\/p>\r\n\r\n<p>\uac19\uc740 $n$\uc774 \uc5ec\ub7ec \ubc88 \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ub3d9\uc6b0\uac00 \uc774\uae30\uba74 <span style=\"color:#e74c3c;\"><code>kidw0124<\/code><\/span>\ub97c, \uc7ac\uc6b0\uac00 \uc774\uae30\uba74 <span style=\"color:#e74c3c;\"><code>eoaud0108<\/code><\/span>\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","subtask1":"<p>$n\\le 20$<\/p>\r\n","subtask2":"<p>$n\\le 1\\,000$<\/p>\r\n","subtask3":"<p>$n\\le 500\\,000$<\/p>\r\n","subtask4":"<p>\ucd94\uac00\uc801\uc778 \uc81c\ud55c \uc870\uac74 \uc5c6\uc74c<\/p>\r\n","sample_explain_1":"<p>$n=4$\uc778 \uacbd\uc6b0 \ub3d9\uc6b0\ub294 \uccab \ubc88\uc9f8 \ud134\uc5d0 \uac00\uc7a5 \ub9c8\uc9c0\ub9c9($4$\ubc88\uc9f8) \uce78\uc5d0 \ub193\uc778 \ub3cc\uc744 \uac00\uc838\uac00\uba74 \uc2b9\ub9ac\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/833c105b-933e-4fa9-a493-d2388aed82f9\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \ud134\uc5d0 \uc7ac\uc6b0\ub294 \ub0a8\uc740 $3$\uce78\uc5d0 \ub193\uc778 \ub3cc\ub4e4 \uc911 \uc774\uc6c3\ud55c $1$\uac1c \ud639\uc740 $2$\uac1c\ub97c \uace8\ub77c \uac00\uc838\uac00\ub294\ub370, \ub2e4\uc74c\uacfc \uac19\uc740 \uacbd\uc6b0\uac00 \uac00\ub2a5\ud558\ub2e4. \uc88c\uc6b0 \ub300\uce6d\uc778 \uc0c1\ud669\uc740 \ud558\ub098\ub9cc \uc0dd\uac01\ud558\uc790.<\/p>\r\n\r\n<ul>\r\n\t<li>$1$ \ud639\uc740 $3$\ubc88 \uce78\uc5d0 \ub193\uc778 \ub3cc\uc744 \uac00\uc838\uac08 \uacbd\uc6b0<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/eaeb6663-d3fc-483d-a0e5-121f8adb1e72\/-\/preview\/\" style=\"height: 160px; width: 211px;\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>$2$\ubc88 \uce78\uc5d0 \ub193\uc778 \ub3cc\uc744 \uac00\uc838\uac08 \uacbd\uc6b0<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\">\u200b\u200b\u200b\u200b\u200b\u200b\u200b<img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/901cd47b-b976-459a-ad4c-3b0dcf5fcaf5\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>$1$, $2$\ubc88 \ud639\uc740 $2$, $3$\ubc88 \uce78\uc5d0 \ub193\uc778 \ub3cc\uc744 \uac00\uc838\uac08 \uacbd\uc6b0 \t\u200b\u200b\u200b\u200b\u200b\u200b\u200b<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\">\u200b\u200b\u200b\u200b\u200b\u200b\u200b<img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/526e4bbe-5bb7-4e8d-a1aa-4d78cb1a4fa5\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uacbd\uc6b0\uc5d0 \ub300\ud574 \ub3d9\uc6b0\ub294 \ub0a8\uc740 \ub3cc\uc744 \uac00\uc838\uac08 \uc218 \uc788\uc73c\uba70, \uc7ac\uc6b0\ub294 \ub124 \ubc88\uc9f8 \ud134\uc744 \uc9c4\ud589\ud560 \uc218 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"31542","problem_lang":"1","title":"1D Stone Game 2","description":"<blockquote>\r\n<p>This problem, compared to <a href=\"\/problem\/31541\">1D Stone Game 1<\/a>, is the same except for the <strong>bold <\/strong>parts.<\/p>\r\n<\/blockquote>\r\n\r\n<p>Dongwoo and Jaewoo are playing a game on a $1\\times n$ gridded board, with one stone placed in each grid.<\/p>\r\n\r\n<p>The game starts with Dongwoo, and the two take turns to take the stones. In other words, Dongwoo plays on the odd turn and Jaewoo plays on the even turn.<\/p>\r\n\r\n<ul>\r\n\t<li>On the first turn, the player picks $1$ grid that has a stone and takes it.<\/li>\r\n\t<li>Starting from the second turn, if the number of stones taken by the other player on the previous turn is $x$, <strong>the player this turn chooses an integer $y$ where $1\\le y\\le x+1$, and then picks $y$ consecutive grids&nbsp;<\/strong>in which the stones are placed and take all the stone placed in the area.<\/li>\r\n\t<li>Whenever stones are taken, if the remaining stones are divided into two parts separated by empty grids, the part with fewer stones are discarded between turns. If the two parts have the same number of stones, any one of two parts is chosen and discarded. If the remaining stones are not divided into two parts, the stones aren&rsquo;t discarded.<\/li>\r\n\t<li>If the player cannot take a stone on his turn according to the conditions, the person loses, and the opponent wins.<\/li>\r\n<\/ul>\r\n\r\n<p>Determine which player wins the game assuming that both players play optimally.<\/p>\r\n","input":"<p>The first line contains a single integer $T$ $(1\\le T\\le 10^6)$ &ndash; the number of test cases. This is followed by the description of the test cases.<\/p>\r\n\r\n<p>The first line of each test case contains a single integer $n$ $(1\\le n\\le 10^{18})$ &ndash; the number of stones initially placed.<\/p>\r\n\r\n<p>Identical test cases don&rsquo;t appear multiple times.<\/p>\r\n","output":"<p>For each test case, output <code><span style=\"color:#e74c3c;\">kidw0124<\/span><\/code> if Dongwoo wins, and <span style=\"color:#e74c3c;\"><code>eoaud0108<\/code><\/span> if Jaewoo wins.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","subtask1":"<p>$n\\le 20$<\/p>\r\n","subtask2":"<p>$n\\le 1\\,000$<\/p>\r\n","subtask3":"<p>$n\\le 500\\,000$<\/p>\r\n","subtask4":"<p>There are no additional restrictions.<\/p>\r\n","sample_explain_1":"<p>When $n=4$, Dongwoo can win by taking the stone placed in the last grid on his first turn.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/833c105b-933e-4fa9-a493-d2388aed82f9\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<p>On the second turn, Jaewoo takes $1$ or $2$ consecutive stones from the remaining $3$ stones, and the following cases are possible. Symmetrical cases are considered as a same case.<\/p>\r\n\r\n<ul>\r\n\t<li>Taking stones on grid number $1$, or grid number $3$<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/eaeb6663-d3fc-483d-a0e5-121f8adb1e72\/-\/preview\/\" style=\"height: 160px; width: 211px;\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>Taking stones on grid number $2$<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\">\u200b\u200b\u200b\u200b\u200b\u200b\u200b<img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/901cd47b-b976-459a-ad4c-3b0dcf5fcaf5\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>Taking stones on grid number $1$ and $2$, or grid number $2$ and $3$<\/li>\r\n<\/ul>\r\n\r\n<p style=\"text-align: center;\">\u200b\u200b\u200b\u200b\u200b\u200b\u200b<img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/526e4bbe-5bb7-4e8d-a1aa-4d78cb1a4fa5\/-\/preview\/\" style=\"width: 211px; height: 160px;\" \/><\/p>\r\n\r\n<p>In all cases, Dongwoo can take the remaining on the third turn, and Jaewoo cannot play the fourth turn.<\/p>\r\n"}]