시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

상근이는 사다리 게임을 하고 있다. 사다리는 n개의 세로줄과 m개의 막대로 이루어져 있다. 세로줄은 왼쪽에서 오른쪽으로 1부터 n까지 번호가 붙어있다. 세로줄 i의 아래에는 양의 정수 si가 적혀있다.

세로줄 i의 상단부터 순서대로 길을 따라가게 되고, 하단에 적혀있는 정수가 그 막대기 i를 선택할 때 얻는 정수이다. 예를 들어, 위의 그림에서 세로줄 1을 선택하면 80점을 얻게 되고, 2를 선택하면 100점을 얻게 된다.

상근이는 세로줄 1부터 세로줄 k까지 연속된 세로줄 k개를 선택한다. 그리고, 선택한 세로줄의 점수의 합계가 상근이의 점수가 된다. 상근이는 막대를 최대 한 개 지울 수 있다. 만약, 막대를 하나 제거한다면, 제거하고 난 이후에 사다리를 타야 한다.

입력으로 사다리의 모양과 선택한 세로줄의 수 k가 주어진다. 이때, 상근이가 얻을 수 있는 가장 작은 점수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 세로줄의 개수 n(2 ≤ n ≤ 1000), 막대의 개수 m(1 ≤ m ≤ 100000), 막대의 길이 h(2 ≤ h ≤ 1000), 상근이가 선택한 세로줄의 수 k(1 ≤ k ≤ n)가 주어진다.

다음 n개 줄에는 세로 막대의 하단에 적혀있는 점수 si가 주어진다. (s1 + s2 + ... + sn ≤ 2×109)

다음 m개 줄에는 막대 i의 위치를 나타내는 ai와 bi가 주어진다. (1 ≤ ai ≤ n-1, 1 ≤ bi ≤ h-1) 막대 i는 세로줄 ai와 ai+1을 연결하고, 상단으로부터의 거리가 bi이다.

출력

첫째 줄에 상근이가 얻을 수 있는 최소 점수를 출력한다.

예제 입력 1

4 5 7 2
20
80
100
50
1 1
2 6
2 3
1 5
3 1

예제 출력 1

100

예제 입력 2

2 2 5 1
10
20
1 1
1 3

예제 출력 2

10

[{"problem_id":"5572","problem_lang":"0","title":"\uc0ac\ub2e4\ub9ac \uac8c\uc784","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc0ac\ub2e4\ub9ac \uac8c\uc784\uc744 \ud558\uace0 \uc788\ub2e4. \uc0ac\ub2e4\ub9ac\ub294 n\uac1c\uc758 \uc138\ub85c\uc904\uacfc m\uac1c\uc758 \ub9c9\ub300\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uc138\ub85c\uc904\uc740 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c 1\ubd80\ud130 n\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\ub2e4. \uc138\ub85c\uc904 i\uc758 \uc544\ub798\uc5d0\ub294 \uc591\uc758 \uc815\uc218 si\uac00 \uc801\ud600\uc788\ub2e4.<\/p>\r\n\r\n<p>\uc138\ub85c\uc904 i\uc758 \uc0c1\ub2e8\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uae38\uc744 \ub530\ub77c\uac00\uac8c \ub418\uace0, \ud558\ub2e8\uc5d0 \uc801\ud600\uc788\ub294 \uc815\uc218\uac00 \uadf8 \ub9c9\ub300\uae30 i\ub97c \uc120\ud0dd\ud560 \ub54c \uc5bb\ub294 \uc815\uc218\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c \uc138\ub85c\uc904 1\uc744 \uc120\ud0dd\ud558\uba74 80\uc810\uc744 \uc5bb\uac8c \ub418\uace0, 2\ub97c \uc120\ud0dd\ud558\uba74 100\uc810\uc744 \uc5bb\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc138\ub85c\uc904 1\ubd80\ud130 \uc138\ub85c\uc904 k\uae4c\uc9c0 \uc5f0\uc18d\ub41c \uc138\ub85c\uc904 k\uac1c\ub97c \uc120\ud0dd\ud55c\ub2e4. \uadf8\ub9ac\uace0, \uc120\ud0dd\ud55c \uc138\ub85c\uc904\uc758 \uc810\uc218\uc758 \ud569\uacc4\uac00 \uc0c1\uadfc\uc774\uc758 \uc810\uc218\uac00 \ub41c\ub2e4. \uc0c1\uadfc\uc774\ub294 \ub9c9\ub300\ub97c \ucd5c\ub300 \ud55c \uac1c \uc9c0\uc6b8 \uc218 \uc788\ub2e4. \ub9cc\uc57d, \ub9c9\ub300\ub97c \ud558\ub098 \uc81c\uac70\ud55c\ub2e4\uba74, \uc81c\uac70\ud558\uace0 \ub09c \uc774\ud6c4\uc5d0 \uc0ac\ub2e4\ub9ac\ub97c \ud0c0\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c \uc0ac\ub2e4\ub9ac\uc758 \ubaa8\uc591\uacfc \uc120\ud0dd\ud55c \uc138\ub85c\uc904\uc758 \uc218 k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub54c, \uc0c1\uadfc\uc774\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 \uc810\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc138\ub85c\uc904\uc758 \uac1c\uc218 n(2 &le; n &le; 1000), \ub9c9\ub300\uc758 \uac1c\uc218 m(1 &le; m &le; 100000), \ub9c9\ub300\uc758 \uae38\uc774 h(2 &le; h &le; 1000), \uc0c1\uadfc\uc774\uac00 \uc120\ud0dd\ud55c \uc138\ub85c\uc904\uc758 \uc218 k(1 &le; k &le; n)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 \uc138\ub85c \ub9c9\ub300\uc758 \ud558\ub2e8\uc5d0 \uc801\ud600\uc788\ub294 \uc810\uc218 s<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (s<sub>1<\/sub> + s<sub>2<\/sub> + ... + s<sub>n<\/sub> &le; 2&times;10<sup>9<\/sup>)<\/p>\r\n\r\n<p>\ub2e4\uc74c m\uac1c \uc904\uc5d0\ub294 \ub9c9\ub300 i\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b4\ub294 a<sub>i<\/sub>\uc640 b<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; a<sub>i<\/sub> &le; n-1, 1 &le; b<sub>i<\/sub> &le; h-1) \ub9c9\ub300 i\ub294 \uc138\ub85c\uc904 a<sub>i<\/sub>\uc640 a<sub>i<\/sub>+1\uc744 \uc5f0\uacb0\ud558\uace0, \uc0c1\ub2e8\uc73c\ub85c\ubd80\ud130\uc758 \uac70\ub9ac\uac00 b<sub>i<\/sub>\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c1\uadfc\uc774\uac00 \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\uc18c \uc810\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/d70be74b-db15-4b95-96e8-2e2cf5e1c05b\/-\/preview\/\" style=\"width: 156px; height: 257px;\" \/><\/p>\r\n","sample_explain_2":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/4e9430f0-e862-427a-b2c5-7d0d050674a2\/-\/preview\/\" style=\"width: 67px; height: 199px;\" \/><\/p>\r\n"},{"problem_id":"5572","problem_lang":"2","title":"\u3042\u307f\u3060\u304f\u3058","description":"<p>\u3042\u306a\u305f\u306f J \u541b\u3068\u4e00\u7dd2\u306b\u3042\u307f\u3060\u304f\u3058\u3092\u4f7f\u3063\u3066\u904a\u3093\u3067\u3044\u308b\uff0e\u3042\u307f\u3060\u304f\u3058\u306f n \u672c\u306e\u7e26\u68d2\u3068m \u672c\u306e\u6a2a\u68d2\u304b\u3089\u306a\u308b\uff0e\u7e26\u68d2\u306b\u306f\u5de6\u304b\u3089\u9806\u306b 1 \u304b\u3089 n \u306e\u756a\u53f7\u304c\u3064\u3044\u3066\u304a\u308a\uff0c\u7e26\u68d2 i \u306e\u4e0b\u7aef\u306b\u306f\u6b63\u6574\u6570 s<sub>i<\/sub> \u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/e468783b-09da-4340-bc3c-9919a9371a3d\/-\/preview\/\" style=\"width: 156px; height: 252px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\u56f3 3-1 \u3042\u307f\u3060\u304f\u3058\u306e\u4f8b\uff08n = 4, m = 5, s<sub>1<\/sub> = 20, s<sub>2<\/sub> = 80, s<sub>3<\/sub> = 100, s<sub>4<\/sub> = 50\uff09<\/p>\r\n\r\n<p>\u7e26\u68d2 i \u306e\u4e00\u756a\u4e0a\u304b\u3089\u9806\u306b\u9053\u3092\u305f\u3069\u3063\u3066\u3044\u304d\u5230\u9054\u3057\u305f\u4e0b\u7aef\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u6574\u6570\u304c\uff0c\u7e26\u68d2 i \u3092\u9078\u3093\u3060\u5834\u5408\u306e\u5f97\u70b9\u3067\u3042\u308b\uff0e\u4f8b\u3048\u3070\uff0c\u56f3 3-1 \u3067\u306f\uff0c\u7e26\u68d2 1 \u3092\u9078\u3076\u3068\u5f97\u70b9\u306f 80 \u70b9\u3067\u3042\u308a\uff0c\u7e26\u68d2 2 \u3092\u9078\u3076\u3068\u5f97\u70b9\u306f 100 \u70b9\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/2f10d16d-9e35-4101-b130-3078fe2c77e4\/-\/preview\/\" style=\"width: 388px; height: 252px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\u56f3 3-2 \u9053\u306e\u305f\u3069\u308a\u65b9\u306e\u4f8b<\/p>\r\n\r\n<p>J \u541b\u306f\u7e26\u68d2 1 \u304b\u3089\u7e26\u68d2 k \u307e\u3067\u306e\u9023\u7d9a\u3057\u305f k \u672c\u3092\u9078\u3076\u3053\u3068\u306b\u3057\u305f\uff0e\u305d\u308c\u3089 k \u672c\u306e\u7e26\u68d2\u3092\u9078\u3093\u3060\u3068\u304d\u306e\u70b9\u6570\u306e\u5408\u8a08\u304c J \u541b\u306e\u5f97\u70b9\u3068\u306a\u308b\uff0e\u305f\u3060\u3057\uff0c\u3042\u306a\u305f\u306f\u3042\u307f\u3060\u304f\u3058\u5185\u306e\u6a2a\u68d2\u3092\u4e00\u672c\u9078\u3073\uff0c\u305d\u306e\u6a2a\u68d2\u3092\u3042\u307f\u3060\u304f\u3058\u304b\u3089\u524a\u9664\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\uff08\u524a\u9664\u3057\u306a\u304f\u3066\u3082\u3088\u3044\uff0e\uff09\u3082\u3057\uff0c\u3042\u306a\u305f\u304c\u6a2a\u68d2\u3092\u4e00\u672c\u524a\u9664\u3057\u305f\u5834\u5408\u306f\uff0c\u524a\u9664\u5f8c\u306e\u3042\u307f\u3060\u304f\u3058\u306b\u304a\u3044\u3066\uff0c\u7e26\u68d2 1 \u304b\u3089\u7e26\u68d2 k \u307e\u3067\u306e\u9023\u7d9a\u3057\u305f k \u672c\u306e\u7e26\u68d2\u3092\u9078\u3093\u3060\u3068\u304d\u306e\u70b9\u6570\u306e\u5408\u8a08\u304c J \u541b\u306e\u5f97\u70b9\u3068\u306a\u308b\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u3068\u3057\u3066\u3042\u307f\u3060\u304f\u3058\u306e\u5f62\u3068 J \u541b\u306e\u9078\u3076\u7e26\u68d2\u306e\u672c\u6570 k \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0cJ \u541b\u306e\u5f97\u70b9\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n","input":"<p>1 \u884c\u76ee\u306b\u306f 4 \u3064\u306e\u6574\u6570 n, m, h, k \u304c\u7a7a\u767d\u533a\u5207\u308a\u3067\u66f8\u304b\u308c\u3066\u3044\u308b\uff0en (2 &le; n &le; 1000) \u306f\u7e26\u68d2\u306e\u672c\u6570\u3092\uff0cm (1 &le; m &le; 100000) \u306f\u6a2a\u68d2\u306e\u672c\u6570\u3092\uff0ch (2 &le; h &le; 1000) \u306f\u7e26\u68d2\u306e\u9577\u3055\u3092\uff0ck (1 &le; k &le; n) \u306f J \u541b\u304c\u9078\u3076\u7e26\u68d2\u306e\u672c\u6570\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u7d9a\u304f n \u884c\u306b\u306f\u7e26\u68d2\u306e\u4e0b\u7aef\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u70b9\u6570\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0ei+1 \u884c\u76ee (1 &le; i &le; n)\u306b\u306f\u6b63\u6574\u6570 s<sub>i<\/sub> \u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u307e\u305f\uff0cs<sub>1<\/sub> + s<sub>2<\/sub> + &middot; &middot; &middot; + s<sub>n<\/sub> &le; 2000000000 = 2 &times; 10<sup>9<\/sup> \u3092\u6e80\u305f\u3059\uff0e<\/p>\r\n\r\n<p>\u7d9a\u304f m \u884c\u306b\u306f\u6a2a\u68d2\u306e\u4f4d\u7f6e\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u6a2a\u68d2\u306b\u306f 1 \u304b\u3089 m \u307e\u3067\u306e\u756a\u53f7\u304c\u3064\u3044\u3066\u3044\u308b\uff0ei + n + 1 \u884c\u76ee (1 &le; i &le; m) \u306b\u306f\uff0c\u6a2a\u68d2 i \u306e\u4f4d\u7f6e\u3092\u8868\u3059 2 \u3064\u306e\u6574\u6570 a<sub>i<\/sub>, b<sub>i<\/sub>(1 &le; a<sub>i<\/sub> &le; n &minus; 1, 1 &le; b<sub>i<\/sub> &le; h &minus; 1) \u304c\u7a7a\u767d\u533a\u5207\u308a\u3067\u66f8\u304b\u308c\u3066\u304a\u308a\uff0c\u6a2a\u68d2 i \u304c\u7e26\u68d2 a<sub>i<\/sub> \u3068\u7e26\u68d2 a<sub>i<\/sub> + 1 \u3092\u7d50\u3073\uff0c\u6a2a\u68d2 i \u306e\u4e0a\u7aef\u304b\u3089\u306e\u8ddd\u96e2\u304c b<sub>i<\/sub> \u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3059\uff0e\u305f\u3060\u3057\uff0c\u3069\u306e 2\u3064\u306e\u6a2a\u68d2\u3082\u7aef\u70b9\u3092\u5171\u6709\u3059\u308b\u3053\u3068\u306f\u306a\u3044\uff0e<\/p>\r\n","output":"<p>\u51fa\u529b\u306fJ \u541b\u306e\u5f97\u70b9\u306e\u6700\u5c0f\u5024\u306e\u307f\u3092\u542b\u3080 1 \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n","hint":"<p>\u4f8b 1 \u306f\u56f3 3-1 \u306b\u5bfe\u5fdc\u3057\uff0c\u3042\u306a\u305f\u304c\u6a2a\u68d2 4 \uff08\u7e26\u68d2 1 \u3068\u7e26\u68d2 2 \u3092\u4e0a\u7aef\u304b\u3089\u8ddd\u96e2 5 \u306e\u5834 \u6240\u3067\u7d50\u3076\u6a2a\u68d2\uff09\u3092\u524a\u9664\u3057\u305f\u3068\u304d\uff0cJ \u541b\u306e\u5f97\u70b9\u306f\u6700\u5c0f\u306b\u306a\u308b\uff0e\u4f8b 2 \u3067\u306f\uff0c\u3042\u306a\u305f\u304c\u6a2a\u68d2 \u3092\u524a\u9664\u3057\u306a\u3044\u5834\u5408\u306b J \u541b\u306e\u5f97\u70b9\u304c\u6700\u5c0f\u306b\u306a\u308b\uff0e\uff08\u56f3 3-3 \u3092\u898b\u3088\uff0e\uff09<\/p>\r\n\r\n<table class=\"table table-bordered td-center td-middle\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td style=\"width:50%;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/d70be74b-db15-4b95-96e8-2e2cf5e1c05b\/-\/preview\/\" style=\"width: 156px; height: 257px;\" \/><\/td>\r\n\t\t\t<td style=\"width:50%;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/4e9430f0-e862-427a-b2c5-7d0d050674a2\/-\/preview\/\" style=\"width: 67px; height: 199px;\" \/><\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p style=\"text-align: center;\">\u56f3 3-3<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]

출처

Olympiad > Japanese Olympiad in Informatics > JOI 2008/2009 3번