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문제

그림 G.1: N명의 입국 승객은 k개의 여권 심사 창구 {Qk} 중 하나를 반드시 거쳐야 한다.

N명의 입국 승객이 여권 심사를 위하여 그림 G.1 과 같이 입국 대기 줄에서 [1, 2, … , N − 1, N] 순서로 기다리고 있다. 입국 승객은 준비된 k개의 여권 심사 창구 중 하나를 통과한 뒤 공항을 빠져나갈 수 있다. 입국할 때의 줄 선 승객의 순서를 [1, 2, … , N − 1, N]이라고 할 때 k개의 여권 심사 창구를 통과하여 입국장을 빠져나가는 순서 [π1, π2, … πN−1, πN]는 처음과 달라질 수 있다. k개 여권 심사 창구가 준비되어 있을 때, 이 입국장을 빠져나가는 순서가 가능한 순서인가를 계산해야 한다.

예를 들어 설명해보자. 만일 N = 3, k = 2라고 할 때 입국장을 빠져나가는 순서 중 [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]는 가능하지만 [3, 2, 1]은 불가능하다. 여러분은 입국장을 빠져나가는 순서 [π1, … , πN]가 입력으로 주어질 때, 이 순서가 가능하면 YES 를, 불가능하면 NO 를 출력해야 한다. 단, 특정 큐에 줄을 선 상황에서는 승객들의 순서를 임의로 바꿀 수는 없다. 그리고 각 여권 심사 창구에 준비된 큐는 N명 승객이 모두 들어올 정도로 충분히 크다고 가정한다.

입력

입력은 표준입력을 사용한다. 첫 번째 줄에는 두 개의 정수 Nk 가 주어진다. N은 입국 승객의 수이며 k는 여권 심사 창구의 수이다. 단, 2 ≤ kN ≤ 100 이다. 그리고 두 번째 줄에는 승객이 입국장을 빠져 나가는 순서 [π1, … , πN]가 주어진다.

출력

출력은 표준출력을 사용한다. 입력으로 주어진 순서 [π1, … , πN]대로 입국장을 빠져나가는 것이 가능하면 YES 를 출력하고, 아니면 NO 를 출력해야 한다.

예제 입력 1

3 2
3 2 1

예제 출력 1

NO

예제 입력 2

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

예제 출력 2

YES
[{"problem_id":"16288","problem_lang":"0","title":"Passport Control","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f56b312b-9138-4a89-a26b-ae3c0be0b1d1\/-\/preview\/\" style=\"width: 382px; height: 234px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\uadf8\ub9bc G.1: <em>N<\/em>\uba85\uc758 \uc785\uad6d \uc2b9\uac1d\uc740 <em>k<\/em>\uac1c\uc758 \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c {<em>Q<\/em><sub><em>k<\/em><\/sub>} \uc911 \ud558\ub098\ub97c \ubc18\ub4dc\uc2dc \uac70\uccd0\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p><em>N<\/em>\uba85\uc758 \uc785\uad6d \uc2b9\uac1d\uc774 \uc5ec\uad8c \uc2ec\uc0ac\ub97c \uc704\ud558\uc5ec \uadf8\ub9bc G.1 \uacfc \uac19\uc774 \uc785\uad6d \ub300\uae30 \uc904\uc5d0\uc11c [1, 2, &hellip; , <em>N<\/em> &minus; 1, <em>N<\/em>] \uc21c\uc11c\ub85c \uae30\ub2e4\ub9ac\uace0 \uc788\ub2e4. \uc785\uad6d \uc2b9\uac1d\uc740 \uc900\ube44\ub41c <em>k<\/em>\uac1c\uc758 \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c \uc911 \ud558\ub098\ub97c \ud1b5\uacfc\ud55c \ub4a4 \uacf5\ud56d\uc744 \ube60\uc838\ub098\uac08 \uc218 \uc788\ub2e4. \uc785\uad6d\ud560 \ub54c\uc758 \uc904 \uc120 \uc2b9\uac1d\uc758 \uc21c\uc11c\ub97c [1, 2, &hellip; , <em>N<\/em> &minus; 1, <em>N<\/em>]\uc774\ub77c\uace0 \ud560 \ub54c <em>k<\/em>\uac1c\uc758 \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c\ub97c \ud1b5\uacfc\ud558\uc5ec \uc785\uad6d\uc7a5\uc744 \ube60\uc838\ub098\uac00\ub294 \uc21c\uc11c [<em>\u03c0<\/em><sub>1<\/sub>, <em>\u03c0<\/em><sub>2<\/sub>, &hellip; <em>\u03c0<\/em><sub><em>N<\/em>&minus;1<\/sub>, <em>\u03c0<\/em><sub><em>N<\/em><\/sub>]\ub294 \ucc98\uc74c\uacfc \ub2ec\ub77c\uc9c8 \uc218 \uc788\ub2e4. <em>k<\/em>\uac1c \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c\uac00 \uc900\ube44\ub418\uc5b4 \uc788\uc744 \ub54c, \uc774 \uc785\uad6d\uc7a5\uc744 \ube60\uc838\ub098\uac00\ub294 \uc21c\uc11c\uac00 \uac00\ub2a5\ud55c \uc21c\uc11c\uc778\uac00\ub97c \uacc4\uc0b0\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 \uc124\uba85\ud574\ubcf4\uc790. \ub9cc\uc77c <em>N<\/em> = 3, <em>k<\/em> = 2\ub77c\uace0 \ud560 \ub54c \uc785\uad6d\uc7a5\uc744 \ube60\uc838\ub098\uac00\ub294 \uc21c\uc11c \uc911 [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]\ub294 \uac00\ub2a5\ud558\uc9c0\ub9cc [3, 2, 1]\uc740 \ubd88\uac00\ub2a5\ud558\ub2e4. \uc5ec\ub7ec\ubd84\uc740 \uc785\uad6d\uc7a5\uc744 \ube60\uc838\ub098\uac00\ub294 \uc21c\uc11c [<em>\u03c0<\/em><sub>1<\/sub>, &hellip; , <em>\u03c0<\/em><sub><em>N<\/em><\/sub>]\uac00 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c8 \ub54c, \uc774 \uc21c\uc11c\uac00 \uac00\ub2a5\ud558\uba74 YES \ub97c, \ubd88\uac00\ub2a5\ud558\uba74 NO \ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4. \ub2e8, \ud2b9\uc815 \ud050\uc5d0 \uc904\uc744 \uc120 \uc0c1\ud669\uc5d0\uc11c\ub294 \uc2b9\uac1d\ub4e4\uc758 \uc21c\uc11c\ub97c \uc784\uc758\ub85c \ubc14\uafc0 \uc218\ub294 \uc5c6\ub2e4. \uadf8\ub9ac\uace0 \uac01 \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c\uc5d0 \uc900\ube44\ub41c \ud050\ub294 <em>N<\/em>\uba85 \uc2b9\uac1d\uc774 \ubaa8\ub450 \ub4e4\uc5b4\uc62c \uc815\ub3c4\ub85c \ucda9\ubd84\ud788 \ud06c\ub2e4\uace0 \uac00\uc815\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \ud45c\uc900\uc785\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ub450 \uac1c\uc758 \uc815\uc218 <em>N<\/em> \uacfc <em>k<\/em> \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. <em>N<\/em>\uc740 \uc785\uad6d \uc2b9\uac1d\uc758 \uc218\uc774\uba70 <em>k<\/em>\ub294 \uc5ec\uad8c \uc2ec\uc0ac \ucc3d\uad6c\uc758 \uc218\uc774\ub2e4. \ub2e8, 2 &le; <em>k<\/em> &le; <em>N<\/em> &le; 100 \uc774\ub2e4. \uadf8\ub9ac\uace0 \ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc2b9\uac1d\uc774 \uc785\uad6d\uc7a5\uc744 \ube60\uc838 \ub098\uac00\ub294 \uc21c\uc11c [<em>\u03c0<\/em><sub>1<\/sub>, &hellip; , <em>\u03c0<\/em><sub><em>N<\/em><\/sub>]\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900\ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc21c\uc11c [<em>\u03c0<\/em><sub>1<\/sub>, &hellip; , <em>\u03c0<\/em><sub><em>N<\/em><\/sub>]\ub300\ub85c \uc785\uad6d\uc7a5\uc744 \ube60\uc838\ub098\uac00\ub294 \uac83\uc774 \uac00\ub2a5\ud558\uba74 <code>YES<\/code> \ub97c \ucd9c\ub825\ud558\uace0, \uc544\ub2c8\uba74 <code>NO<\/code> \ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"16288","problem_lang":"1","title":"Passport Control","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f56b312b-9138-4a89-a26b-ae3c0be0b1d1\/-\/preview\/\" style=\"width: 382px; height: 234px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure G.1: <em>N<\/em> passengers should be controlled at one of the passport control offices {<em>Q<\/em><sub><em>k<\/em><\/sub>}.<\/p>\r\n\r\n<p>All <em>N<\/em> passengers wait in one immigration queue for the passport control in the order of [1, 2, 3, &hellip; , <em>N<\/em> &minus; 1, <em>N<\/em>] as shown in Figure G.1. Each passenger is required to be checked at one of <em>k<\/em> passport control queues. After completing the passport control, the passenger exits from the airport through the exit gate (Exit as shown in Figure G.1). The initial order of the entrance queue, [1, 2, 3, &hellip; , <em>N<\/em> &minus; 1, <em>N<\/em>] can be changed to a shuffled order, [<em>\u03c0<\/em><sub>1<\/sub>, <em>\u03c0<\/em><sub>2<\/sub>, &hellip; <em>\u03c0<\/em><sub><em>N<\/em>&minus;1<\/sub>, <em>\u03c0<\/em><sub><em>N<\/em><\/sub>] at the exit gate. You must determine if the exiting order [<em>\u03c0<\/em><sub>1<\/sub>, <em>\u03c0<\/em><sub>2<\/sub>, &hellip; <em>\u03c0<\/em><sub><em>N<\/em>&minus;1<\/sub>, <em>\u03c0<\/em><sub><em>N<\/em><\/sub>] is possible using k parallel passport control queues. Let us explain with an example. In the case of <em>N<\/em> = 3 and <em>k<\/em> = 2, the exit orders [1, 2, 3],[1, 3, 2],[2, 1, 3],[2, 3, 1],[3, 1, 2] are all possible, but [3, 2, 1] is not.<\/p>\r\n\r\n<p>Given an exit order [<em>\u03c0<\/em><sub>1<\/sub>, &hellip; , <em>\u03c0<\/em><sub><em>N<\/em><\/sub>] as an input, write a program to print <code>YES<\/code> if the exit order is possible, or <code>NO<\/code> if not. Note that passengers are not allowed to change their order in passport control queues and each control queue is long enough to keep all <em>N<\/em> passengers.<\/p>\r\n","input":"<p>Your program is to read from standard input. The standard input consists of two lines. The first line gives two integers, <em>N<\/em> and <em>k<\/em>, where <em>N<\/em> is the number of passengers and k is the number of passport control queues. Note that 2 &le; <em>k<\/em> &le; <em>N<\/em> &le; 100. The second line gives [<em>\u03c0<\/em><sub>1<\/sub>, &hellip; , <em>\u03c0<\/em><sub><em>N<\/em><\/sub>], an exit order of the passengers from the airport<\/p>\r\n","output":"<p>Your program is to write to standard output. Print the string <code>YES<\/code> if the exit order is possible or <code>NO<\/code> otherwise.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]