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2 초 512 MB51946543492.144%

문제

교실에는 N명의 학생들이 한 줄로 서 있다. 각 학생들은 번호표를 하나씩 가지고 있다. i번째 학생의 번호표에 적힌 수는 Ai이다.

그리고 M개의 카드가 있다. 이 카드는 1부터 M까지의 값을 가진다. 각 카드는 반드시 1부터 사용하며, k (2 ≤ k ≤ M) 번 카드는 k-1번 카드를 쓴 다음에 쓴다.

게임의 규칙은 다음과 같다.

  • 선생님이 1번 학생에게 i번 카드를 준다. (1 ≤ i ≤ M)
  • 카드를 받은 j번 학생은 j+1번 학생에게 카드를 넘긴다.
  • Aj % i의 값이 Aj+1%i 의 값보다 크면 두 학생의 번호표를 서로 교환한다.
  • 마지막 학생이 카드를 받으면 그 카드는 버린다.

이 과정은 마지막 M번 카드까지 버리면 끝난다.

이 과정을 모두 마친 후의 각 학생들이 가진 번호표를 순서대로 출력하는 프로그램을 작성하시오.

입력

첫 번째 줄에 학생의 수와 카드의 수를 나타내는 정수 N, M (1 ≤ N ≤ 100, 1 ≤ M ≤ 100) 이 공백으로 구분되어 입력된다.

두 번째 줄부터 N줄에 걸쳐서 각 학생이 가지는 번호표의 값 Ai (1 ≤ Ai ≤ 1000) 가 주어진다.

출력

게임이 종료된 후에 각 학생이 가지는 번호표의 값을 한 줄에 하나씩 출력한다.

예제 입력 1

6 4
3
2
8
3
1
5

예제 출력 1

2
3
1
8
5
3

예제 입력 2

10 6
1
2
3
4
5
6
7
8
9
10

예제 출력 2

6
1
2
3
10
4
8
7
9
5

힌트

1번 예제에서

  • 1번 카드를 사용한 후의 학생들의 번호표 : 3 2 8 3 1 5
  • 2번 카드를 사용한 후의 학생들의 번호표 : 2 8 3 3 1 5
  • 3번 카드를 사용한 후의 학생들의 번호표 : 2 3 3 1 8 5
  • 4번 카드를 사용한 후의 학생들의 번호표 : 2 3 1 8 5 3

따라서 2 3 1 8 5 3 이 된다.

[{"problem_id":"11949","problem_lang":"0","title":"\ubc88\ud638\ud45c \uad50\ud658","description":"<p>\uad50\uc2e4\uc5d0\ub294 N\uba85\uc758 \ud559\uc0dd\ub4e4\uc774 \ud55c \uc904\ub85c \uc11c \uc788\ub2e4. \uac01 \ud559\uc0dd\ub4e4\uc740 \ubc88\ud638\ud45c\ub97c \ud558\ub098\uc529 \uac00\uc9c0\uace0 \uc788\ub2e4. i\ubc88\uc9f8 \ud559\uc0dd\uc758 \ubc88\ud638\ud45c\uc5d0 \uc801\ud78c \uc218\ub294 A<sub>i<\/sub>\uc774\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 M\uac1c\uc758 \uce74\ub4dc\uac00 \uc788\ub2e4. \uc774 \uce74\ub4dc\ub294 1\ubd80\ud130 M\uae4c\uc9c0\uc758 \uac12\uc744 \uac00\uc9c4\ub2e4. \uac01 \uce74\ub4dc\ub294 \ubc18\ub4dc\uc2dc 1\ubd80\ud130 \uc0ac\uc6a9\ud558\uba70, k (2 &le; k &le; M) \ubc88 \uce74\ub4dc\ub294 k-1\ubc88 \uce74\ub4dc\ub97c \uc4f4 \ub2e4\uc74c\uc5d0 \uc4f4\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc758 \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc120\uc0dd\ub2d8\uc774 1\ubc88 \ud559\uc0dd\uc5d0\uac8c i\ubc88 \uce74\ub4dc\ub97c \uc900\ub2e4. (1 &le; i &le;&nbsp;M)<\/li>\r\n\t<li>\uce74\ub4dc\ub97c \ubc1b\uc740 j\ubc88 \ud559\uc0dd\uc740 j+1\ubc88 \ud559\uc0dd\uc5d0\uac8c \uce74\ub4dc\ub97c \ub118\uae34\ub2e4.<\/li>\r\n\t<li>A<sub>j<\/sub> % i\uc758 \uac12\uc774 A<sub>j+1<\/sub>%i \uc758 \uac12\ubcf4\ub2e4 \ud06c\uba74 \ub450 \ud559\uc0dd\uc758 \ubc88\ud638\ud45c\ub97c \uc11c\ub85c \uad50\ud658\ud55c\ub2e4.<\/li>\r\n\t<li>\ub9c8\uc9c0\ub9c9 \ud559\uc0dd\uc774 \uce74\ub4dc\ub97c \ubc1b\uc73c\uba74 \uadf8 \uce74\ub4dc\ub294 \ubc84\ub9b0\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774 \uacfc\uc815\uc740 \ub9c8\uc9c0\ub9c9 M\ubc88 \uce74\ub4dc\uae4c\uc9c0 \ubc84\ub9ac\uba74 \ub05d\ub09c\ub2e4.<\/p>\r\n\r\n<p><span style=\"line-height:1.6em\">\uc774 \uacfc\uc815\uc744 \ubaa8\ub450 \ub9c8\uce5c \ud6c4\uc758 \uac01 \ud559\uc0dd\ub4e4\uc774 \uac00\uc9c4 \ubc88\ud638\ud45c\ub97c \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/span><\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud559\uc0dd\uc758 \uc218\uc640 \uce74\ub4dc\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218&nbsp;N, M (1 &le;&nbsp;N &le;&nbsp;100, 1 &le; M &le; 100) \uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc785\ub825\ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 N\uc904\uc5d0 \uac78\uccd0\uc11c \uac01 \ud559\uc0dd\uc774 \uac00\uc9c0\ub294 \ubc88\ud638\ud45c\uc758 \uac12 A<sub>i<\/sub> (1 &le; A<sub>i<\/sub> &le; 1000) \uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac8c\uc784\uc774 \uc885\ub8cc\ub41c \ud6c4\uc5d0 \uac01 \ud559\uc0dd\uc774 \uac00\uc9c0\ub294 \ubc88\ud638\ud45c\uc758 \uac12\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>1\ubc88 \uc608\uc81c\uc5d0\uc11c<\/p>\r\n\r\n<ul>\r\n\t<li>1\ubc88 \uce74\ub4dc\ub97c \uc0ac\uc6a9\ud55c \ud6c4\uc758 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\ud45c : 3 2 8 3 1 5<\/li>\r\n\t<li>2\ubc88 \uce74\ub4dc\ub97c \uc0ac\uc6a9\ud55c \ud6c4\uc758 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\ud45c : 2 8 3 3 1 5<\/li>\r\n\t<li>3\ubc88 \uce74\ub4dc\ub97c \uc0ac\uc6a9\ud55c \ud6c4\uc758 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\ud45c : 2 3 3 1 8 5<\/li>\r\n\t<li>4\ubc88 \uce74\ub4dc\ub97c \uc0ac\uc6a9\ud55c \ud6c4\uc758 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\ud45c : 2 3 1 8 5 3<\/li>\r\n<\/ul>\r\n\r\n<p>\ub530\ub77c\uc11c 2 3 1 8 5 3 \uc774 \ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"11949","problem_lang":"2","title":"\u30bc\u30c3\u30b1\u30f3\u306e\u4ea4\u63db (Swapping Bibs)","description":"<p>JOI \u9ad8\u6821\u306e N \u4eba\u306e\u751f\u5f92\u304c\u6771\u897f\u306b\u4e00\u5217\u306b\u4e26\u3093\u3067\u3044\u308b\uff0e\u5217\u306e\u897f\u306e\u7aef\u304b\u3089 i \u756a\u76ee\u306e\u751f\u5f92\u304c\u751f\u5f92 i \u3067\u3042\u308b\uff0e\u305d\u308c\u305e\u308c\u306e\u751f\u5f92\u306f\u6574\u6570\u304c 1 \u3064\u66f8\u304b\u308c\u305f\u30bc\u30c3\u30b1\u30f3\u3092\u4ed8\u3051\u3066\u3044\u308b\uff0e\u6700\u521d\uff0c\u751f\u5f92 i \u306e\u30bc\u30c3\u30b1\u30f3\u306b\u306f\u6574\u6570 A<sub>i<\/sub> \u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>\u30d0\u30c8\u30f3\u304c M \u500b\u3042\u308a\uff0c\u30d0\u30c8\u30f3\u306b\u306f 1 \u304b\u3089 M \u307e\u3067\u306e\u756a\u53f7\u304c\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\uff0ek = 1, 2, ..., M \u306b\u5bfe\u3057\uff0c\u4ee5\u4e0b\u306e\u64cd\u4f5c\u3092\u884c\u3046\uff0e\u30d0\u30c8\u30f3 k (2 \u2266 k \u2266 M) \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u306f\uff0c\u30d0\u30c8\u30f3 k - 1 \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u304c\u7d42\u308f\u3063\u3066\u304b\u3089\u884c\u3046\uff0e<\/p>\r\n\r\n<ol>\r\n\t<li>\u5148\u751f\u304c\u30d0\u30c8\u30f3 k \u3092\u751f\u5f92 1 \u306b\u6e21\u3059\uff0e<\/li>\r\n\t<li>\u30d0\u30c8\u30f3\u3092\u53d7\u3051\u53d6\u3063\u305f\u751f\u5f92\u306f\uff0c\u4ee5\u4e0b\u306e\u30eb\u30fc\u30eb\u306b\u5f93\u3063\u3066\u30d0\u30c8\u30f3\u3092\u6e21\u3059\uff0e\r\n\t<ul>\r\n\t\t<li>\u30eb\u30fc\u30eb\uff1a\u751f\u5f92 i \u304c\u30d0\u30c8\u30f3 k \u3092\u53d7\u3051\u53d6\u3063\u305f\u3068\u3059\u308b\uff0e\r\n\t\t<ul>\r\n\t\t\t<li>1 \u2266 i \u2266 N - 1 \u306e\u3068\u304d: \u751f\u5f92 i \u306e\u30bc\u30c3\u30b1\u30f3\u306e\u6574\u6570\u3092 k \u3067\u5272\u3063\u305f\u4f59\u308a\u304c\uff0c\u751f\u5f92 i + 1 \u306e\u30bc\u30c3\u30b1\u30f3\u306e\u6574\u6570\u3092 k \u3067\u5272\u3063\u305f\u4f59\u308a\u3088\u308a\u3082\u5927\u304d\u3044\u3068\u304d\uff0c\u751f\u5f92 i \u3068\u751f\u5f92 i + 1 \u304c\u30bc\u30c3\u30b1\u30f3\u3092\u4ea4\u63db\u3057\uff0c\u751f\u5f92 i \u306f\u751f\u5f92 i + 1 \u306b\u30d0\u30c8\u30f3\u3092\u6e21\u3059\uff0e\u305d\u3046\u3067\u306a\u3044\u3068\u304d\u306f\uff0c\u30bc\u30c3\u30b1\u30f3\u3092\u4ea4\u63db\u305b\u305a\u306b\uff0c\u751f\u5f92 i \u306f\u751f\u5f92 i + 1 \u306b\u30d0\u30c8\u30f3\u3092\u6e21\u3059\uff0e<\/li>\r\n\t\t\t<li>i = N \u306e\u3068\u304d: \u751f\u5f92 N \u306f\u30d0\u30c8\u30f3\u3092\u5148\u751f\u306b\u6e21\u3059\uff0e<\/li>\r\n\t\t<\/ul>\r\n\t\t<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n\t<li>\u5148\u751f\u304c\u751f\u5f92 N \u304b\u3089\u30d0\u30c8\u30f3 k \u3092\u53d7\u3051\u53d6\u3063\u305f\u3089\uff0c\u30d0\u30c8\u30f3 k \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u306f\u7d42\u308f\u308a\u3067\u3042\u308b\uff0e<\/li>\r\n<\/ol>\r\n\r\n<p>\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306b\u6700\u521d\u306b\u66f8\u304b\u308c\u3066\u3044\u305f\u6574\u6570\u3068\u30d0\u30c8\u30f3\u306e\u500b\u6570 M \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u5148\u751f\u304c\u751f\u5f92 N \u304b\u3089\u30d0\u30c8\u30f3 M \u3092\u53d7\u3051\u53d6\u3063\u305f\u5f8c\u306e\uff0c\u305d\u308c\u305e\u308c\u306e\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306e\u6574\u6570\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u306f 1 + N \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n\r\n<p>1 \u884c\u76ee\u306b\u306f\u6574\u6570 N, M (1 \u2266 N \u2266 100, 1 \u2266 M \u2266 100) \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u304a\u308a\uff0c\u305d\u308c\u305e\u308c\u751f\u5f92\u306e\u4eba\u6570\u3068\u30d0\u30c8\u30f3\u306e\u500b\u6570\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u7d9a\u304f N \u884c\u306e\u3046\u3061\u306e i \u884c\u76ee (1 \u2266 i \u2266 N) \u306b\u306f\u6574\u6570 A<sub>i<\/sub> (1 \u2266 A<sub>i<\/sub> \u2266 1000) \u304c\u66f8\u304b\u308c\u3066\u304a\u308a\uff0c\u751f\u5f92 i \u306e\u30bc\u30c3\u30b1\u30f3\u306b\u6700\u521d\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u6574\u6570 A<sub>i<\/sub> \u3092\u8868\u3059\uff0e<\/p>\r\n","output":"<p>\u51fa\u529b\u306f N \u884c\u304b\u3089\u306a\u308b\uff0ei \u884c\u76ee (1 \u2266 i \u2266 N) \u306b\u306f\uff0c\u5148\u751f\u304c\u751f\u5f92 N \u304b\u3089\u30d0\u30c8\u30f3 M \u3092\u53d7\u3051\u53d6\u3063\u305f\u5f8c\u306e\uff0c\u751f\u5f92 i \u306e\u30bc\u30c3\u30b1\u30f3\u306e\u6574\u6570\u3092\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n","hint":"<p>\u5165\u51fa\u529b\u4f8b 1 \u3067\u306f 6 \u4eba\u306e\u751f\u5f92\u304c\u3044\u308b\uff0e\u6700\u521d\uff0c\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306f\u9806\u306b 3\uff0c 2\uff0c 8\uff0c 3\uff0c 1\uff0c 5 \u3067\u3042\u308b\uff0e\u30d0\u30c8\u30f3\u306f 4 \u500b\u3042\u308b\uff0e<\/p>\r\n\r\n<ul>\r\n\t<li>\u30d0\u30c8\u30f3 1 \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u304c\u7d42\u4e86\u3057\u305f\u6642\u70b9\u3067\u306e\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306f\u9806\u306b 3\uff0c 2\uff0c 8\uff0c 3\uff0c 1\uff0c 5 \u3067\u3042\u308b\uff0e<\/li>\r\n\t<li>\u30d0\u30c8\u30f3 2 \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u304c\u7d42\u4e86\u3057\u305f\u6642\u70b9\u3067\u306e\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306f\u9806\u306b 2\uff0c 8\uff0c 3\uff0c 3\uff0c 1\uff0c 5 \u3067\u3042\u308b\uff0e<\/li>\r\n\t<li>\u30d0\u30c8\u30f3 3 \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u304c\u7d42\u4e86\u3057\u305f\u6642\u70b9\u3067\u306e\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306f\u9806\u306b 2\uff0c 3\uff0c 3\uff0c 1\uff0c 8\uff0c 5 \u3067\u3042\u308b\uff0e<\/li>\r\n\t<li>\u30d0\u30c8\u30f3 4 \u306b\u95a2\u3059\u308b\u64cd\u4f5c\u304c\u7d42\u4e86\u3057\u305f\u6642\u70b9\u3067\u306e\u751f\u5f92\u306e\u30bc\u30c3\u30b1\u30f3\u306f\u9806\u306b 2\uff0c 3\uff0c 1\uff0c 8\uff0c 5\uff0c 3 \u3067\u3042\u308b\uff0e<\/li>\r\n<\/ul>\r\n\r\n<p>\u203b\u5404\u5165\u51fa\u529b\u4f8b\u306e\u30c7\u30fc\u30bf\u306f\uff0c\u53f3\u30af\u30ea\u30c3\u30af\u7b49\u306b\u3088\u308a\u30d5\u30a1\u30a4\u30eb\u306b\u4fdd\u5b58\u3057\u3066\u5229\u7528\u53ef\u80fd\u3067\u3059\uff0e<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]

출처

Olympiad > Japanese Olympiad in Informatics > Japanese Olympiad in Informatics Qualification Round > JOI 2015/2016 예선 2번