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문제

홍준이는 오래된 울타리를 색칠해야한다. 이 울타리는 너비가 1cm이고 높이가 여러 가지인 널빤지 N개로 만들어졌다. 색칠을 빨리 하기 위해, 홍준이는 롤러 Super Paint Roller Deluxe를 샀다. 이 롤러의 폭은 X cm이다. 홍준이는 색칠을 할 때, 롤러의 모든 부분이 널빤지를 벗어나지않게 해야한다. 그렇지 않으면 페인트가 흘러서 주위를 얼룩지게 할 수 있다. 또한, 색칠 중에 롤러는 언제나 땅과 평행해야한다. 즉, 홍준이가 롤러를 안전하게 쓰기 위해서는, X개의 연속된 널빤지를 선택해서 맨 밑에서부터 X개의 널빤지 중 가장 높이가 낮은 널빤지 전체를 색칠할 때까지, 한 번에 색칠해야한다. 그 다음 다른 X개의 널빤지를 선택해서, 같은 방법으로 칠하는 작업을 반복한다.

이렇게 색칠하면 널빤지의 몇 부분이 색칠되지 않으므로, 홍준이는 그 부분을 칫솔로 페인트칠 해야한다. 이건 누구나 알다시피 지루한 작업이기 때문에, 홍준이는 여러분에게 Super Paint Roller Deluxe를 이용해서 가장 많은 영역을 색칠할 수 있도록 도움을 요청했다. 이러한 방법이 여러 가지 있다면, 홍준이는 최소한의 롤러질 횟수로 색칠하려고한다. 홍준이를 도와, 칫솔로 칠해야 할 널빤지의 최소 넓이와 최소 롤러질 횟수를 구하는 프로그램을 작성하시오.

입력

첫 번째 줄에 널빤지의 수 N (1 ≤ N ≤ 1 000 000), Super Paint Roller Deluxe의 너비 X (1 ≤ X ≤ 100 000, X ≤ N)가 주어진다.

두 번째 줄에 널빤지들의 높이를 의미하는 1 000 000 이하의 자연수 N개가 주어진다.

출력

첫 번째 줄에 홍준이가 칫솔로 칠해야하는 널빤지 넓이의 최솟값을 출력한다.

두 번째 줄에 이때 필요한 최소한의 롤러질 횟수를 출력한다.

예제 입력 1

5 3
5 3 4 4 5

예제 출력 1

3
2

홍준이는 두 번의 롤러질을 한다. - 1, 2, 3번째 널빤지에 높이 3cm로, 나머지 3, 4, 5번째 널빤지에는 높이 4cm로 칠한다. 3cm²(2cm²는 1번 널빤지, 1cm²는 5번 널빤지)가 칠해지지 않아서 칫솔로 칠해야한다. 그리고 가운데 3번째 널빤지에 3cm²이 2번 중복되어서 칠해졌지만, 상관없다.

예제 입력 2

10 3
3 3 3 3 3 3 3 3 3 3

예제 출력 2

0
4

예제 입력 3

7 4
1 2 3 4 3 2 1

예제 출력 3

4
4
[{"problem_id":"2905","problem_lang":"0","title":"\ud64d\uc900\uc774\uc640 \uc6b8\ud0c0\ub9ac","description":"<p>\ud64d\uc900\uc774\ub294 \uc624\ub798\ub41c \uc6b8\ud0c0\ub9ac\ub97c \uc0c9\uce60\ud574\uc57c\ud55c\ub2e4. \uc774 \uc6b8\ud0c0\ub9ac\ub294 \ub108\ube44\uac00 1cm\uc774\uace0 \ub192\uc774\uac00 \uc5ec\ub7ec \uac00\uc9c0\uc778 \ub110\ube64\uc9c0 N\uac1c\ub85c \ub9cc\ub4e4\uc5b4\uc84c\ub2e4. \uc0c9\uce60\uc744&nbsp;\ube68\ub9ac \ud558\uae30 \uc704\ud574, \ud64d\uc900\uc774\ub294 \ub864\ub7ec Super Paint Roller Deluxe\ub97c \uc0c0\ub2e4. \uc774 \ub864\ub7ec\uc758 \ud3ed\uc740 X cm\uc774\ub2e4. \ud64d\uc900\uc774\ub294 \uc0c9\uce60\uc744 \ud560 \ub54c, \ub864\ub7ec\uc758 \ubaa8\ub4e0 \ubd80\ubd84\uc774 \ub110\ube64\uc9c0\ub97c \ubc97\uc5b4\ub098\uc9c0\uc54a\uac8c&nbsp;\ud574\uc57c\ud55c\ub2e4. \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74&nbsp;\ud398\uc778\ud2b8\uac00 \ud758\ub7ec\uc11c \uc8fc\uc704\ub97c \uc5bc\ub8e9\uc9c0\uac8c \ud560 \uc218 \uc788\ub2e4. \ub610\ud55c, \uc0c9\uce60&nbsp;\uc911\uc5d0 \ub864\ub7ec\ub294 \uc5b8\uc81c\ub098 \ub545\uacfc \ud3c9\ud589\ud574\uc57c\ud55c\ub2e4. \uc989, \ud64d\uc900\uc774\uac00 \ub864\ub7ec\ub97c \uc548\uc804\ud558\uac8c \uc4f0\uae30 \uc704\ud574\uc11c\ub294, X\uac1c\uc758 \uc5f0\uc18d\ub41c \ub110\ube64\uc9c0\ub97c \uc120\ud0dd\ud574\uc11c \ub9e8 \ubc11\uc5d0\uc11c\ubd80\ud130 X\uac1c\uc758 \ub110\ube64\uc9c0 \uc911 \uac00\uc7a5 \ub192\uc774\uac00 \ub0ae\uc740 \ub110\ube64\uc9c0 \uc804\uccb4\ub97c \uc0c9\uce60\ud560 \ub54c\uae4c\uc9c0, \ud55c \ubc88\uc5d0 \uc0c9\uce60\ud574\uc57c\ud55c\ub2e4. \uadf8 \ub2e4\uc74c&nbsp;\ub2e4\ub978 X\uac1c\uc758 \ub110\ube64\uc9c0\ub97c \uc120\ud0dd\ud574\uc11c, \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uce60\ud558\ub294 \uc791\uc5c5\uc744 \ubc18\ubcf5\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub807\uac8c \uc0c9\uce60\ud558\uba74&nbsp;\ub110\ube64\uc9c0\uc758 \uba87 \ubd80\ubd84\uc774 \uc0c9\uce60\ub418\uc9c0 \uc54a\uc73c\ubbc0\ub85c, \ud64d\uc900\uc774\ub294 \uadf8 \ubd80\ubd84\uc744 \uce6b\uc194\ub85c \ud398\uc778\ud2b8\uce60&nbsp;\ud574\uc57c\ud55c\ub2e4. \uc774\uac74 \ub204\uad6c\ub098 \uc54c\ub2e4\uc2dc\ud53c \uc9c0\ub8e8\ud55c \uc791\uc5c5\uc774\uae30 \ub54c\ubb38\uc5d0, \ud64d\uc900\uc774\ub294 \uc5ec\ub7ec\ubd84\uc5d0\uac8c Super Paint Roller Deluxe\ub97c \uc774\uc6a9\ud574\uc11c \uac00\uc7a5 \ub9ce\uc740 \uc601\uc5ed\uc744 \uc0c9\uce60\ud560 \uc218 \uc788\ub3c4\ub85d \ub3c4\uc6c0\uc744 \uc694\uccad\ud588\ub2e4. \uc774\ub7ec\ud55c \ubc29\ubc95\uc774 \uc5ec\ub7ec \uac00\uc9c0 \uc788\ub2e4\uba74, \ud64d\uc900\uc774\ub294&nbsp;\ucd5c\uc18c\ud55c\uc758 \ub864\ub7ec\uc9c8 \ud69f\uc218\ub85c \uc0c9\uce60\ud558\ub824\uace0\ud55c\ub2e4. \ud64d\uc900\uc774\ub97c \ub3c4\uc640, \uce6b\uc194\ub85c \uce60\ud574\uc57c&nbsp;\ud560 \ub110\ube64\uc9c0\uc758 \ucd5c\uc18c \ub113\uc774\uc640 \ucd5c\uc18c \ub864\ub7ec\uc9c8 \ud69f\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ub110\ube64\uc9c0\uc758 \uc218 N (1 &le; N &le; 1 000 000), Super Paint Roller Deluxe\uc758 \ub108\ube44 X (1 &le; X &le;&nbsp;100 000, X &le; N)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 \ub110\ube64\uc9c0\ub4e4\uc758 \ub192\uc774\ub97c \uc758\ubbf8\ud558\ub294 1 000 000 \uc774\ud558\uc758 \uc790\uc5f0\uc218 N\uac1c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ud64d\uc900\uc774\uac00 \uce6b\uc194\ub85c \uce60\ud574\uc57c\ud558\ub294&nbsp;\ub110\ube64\uc9c0 \ub113\uc774\uc758 \ucd5c\uc19f\uac12\uc744&nbsp;\ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 \uc774\ub54c&nbsp;\ud544\uc694\ud55c \ucd5c\uc18c\ud55c\uc758 \ub864\ub7ec\uc9c8 \ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/29c40fb8-8aeb-45b9-8b57-17a41bb907cf\/-\/crop\/503x508\/3,2\/-\/preview\/\" style=\"width: 252px; height: 254px; float: right;\" \/>\ud64d\uc900\uc774\ub294 \ub450 \ubc88\uc758 \ub864\ub7ec\uc9c8\uc744 \ud55c\ub2e4. - 1, 2, 3\ubc88\uc9f8 \ub110\ube64\uc9c0\uc5d0 \ub192\uc774 3cm\ub85c, \ub098\uba38\uc9c0 3, 4, 5\ubc88\uc9f8&nbsp;\ub110\ube64\uc9c0\uc5d0\ub294 \ub192\uc774 4cm\ub85c \uce60\ud55c\ub2e4. 3cm&sup2;(2cm&sup2;\ub294 1\ubc88 \ub110\ube64\uc9c0, 1cm&sup2;\ub294 5\ubc88 \ub110\ube64\uc9c0)\uac00 \uce60\ud574\uc9c0\uc9c0 \uc54a\uc544\uc11c \uce6b\uc194\ub85c \uce60\ud574\uc57c\ud55c\ub2e4. \uadf8\ub9ac\uace0 \uac00\uc6b4\ub370 3\ubc88\uc9f8 \ub110\ube64\uc9c0\uc5d0 3cm&sup2;\uc774 2\ubc88&nbsp;\uc911\ubcf5\ub418\uc5b4\uc11c \uce60\ud574\uc84c\uc9c0\ub9cc, \uc0c1\uad00\uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"2905","problem_lang":"1","title":"OGRADA","description":"<p>Matija needs to paint his old fence. The fence is made from N planks, each 1 cm in width and varying in height. To do this easy and fast, he bought himself a Super Paint Roller Deluxe. The paint roller is X cm wide. The Super Paint Roller Deluxe model comes with a catch, however. Matija must at all times touch the planks with full width of the roller, otherwise paint drops all around and stains everything. Also, the roller must always be parallel to the ground to prevent leakage. This means that in order for Matija to use the roller safely, he needs to select X planks, and paint them from bottom to the top of the lowest plank in one swoop. Then he selects some other X planks, paints them and so on.<\/p>\r\n\r\n<p>This leaves parts of some planks unpainted. Matija will have to paint such parts with a toothbrush. This is obviously quite tedious so he asked you to help him paint as much as possible using the Super Paint Roller Deluxe. Since there is more than one way to do this he is also interested in the painting that requires the minimal number of swoops.<\/p>\r\n","input":"<p>The first line of input contains two integers N (1 &le; N &le; 1 000 000), number of planks, and X (1 &le; X &le; 100 000), width of the Super Paint Roller. Width of the Super Paint<\/p>\r\n\r\n<p>Roller will not exceed the width of the fence. The second line of input contains N positive integers, smaller than 1 000 000, heights of planks in the fence.<\/p>\r\n","output":"<p>The first line of output should contain the smallest possible area Matija will have to paint manually.<\/p>\r\n\r\n<p>The second line of output should contain the smallest number of swoops needed.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/29c40fb8-8aeb-45b9-8b57-17a41bb907cf\/-\/crop\/503x508\/3,2\/-\/preview\/\" style=\"width: 252px; height: 254px; float: right;\" \/>Matija needs two swoops with his roller - one to paint planks 1, 2 and 3 to the height of 3 cm, the other to paint planks 3, 4 and 5 to the height of 4 cm. Note that 3 cm<sup>2<\/sup> (2 cm<sup>2<\/sup> on plank 1 and 1 cm<sup>2<\/sup> on plank 5) are left unpainted. Also, 3 cm<sup>2<\/sup> on plank 3 are painted over twice, but that&#39;s OK.<\/p>\r\n"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2009/2010 > Contest #4 4번