문제
은하는 열심히 일한 덕에 드디어 새 차를 뽑았습니다! 시운전으로 일직선 도로를 따라 차를 타고 목적지로 이동하려 합니다. 목적지까지 거리가 꽤 되기 때문에, 중간중간 주유소에서 연료를 넣으려고 합니다. 시운전 중에는 다음과 같은 조건을 지켜야 합니다.
- $i$번째 주유소는 길의 원점으로부터 오른쪽으로 $x_{i}$킬로미터 떨어진 위치에 있으며, 이 주유소에서 차에 넣을 수 있는 연료는 리터 당 단가가 $p_{i}$이고 총 $a_{i}$리터만큼의 연료가 있습니다.
- 주유소에서는 연료를 $a_{i}$리터 이하로 원하는 만큼 주유할 수 있습니다.
- 각 주유소에서 주유한 뒤 차에 들어 있는 연료의 양이 차의 연료 용량인 $F$리터를 넘겨서는 안 됩니다.
- 차는 1ドル$리터의 연료로 1ドル$킬로미터를 움직일 수 있습니다.
- 새 차는 시운전 전에는 연료가 없습니다. 따라서 차의 시작 지점은 첫 번째 주유소입니다.
- 목적지는 길의 원점으로부터 오른쪽으로 $X$킬로미터 떨어진 위치입니다.
은하는 열심히 번 돈을 연료에 쓰는 것은 아까워, 목적지까지 최소 비용으로 이동하려 합니다. 여러분은 은하를 도와 주어야 합니다!
출력
어떤 경로로 시운전을 진행해도 목적지에 도달할 수 없으면 첫째 줄에 -1을 출력합니다. 그렇지 않으면 첫째 줄에 시운전을 마치는 데 드는 최소 비용을 출력합니다.
[{"problem_id":"31398","problem_lang":"0","title":"\uac00\uc2a4 \ucda9\uc804\uc18c","description":"<p>\uc740\ud558\ub294 \uc5f4\uc2ec\ud788 \uc77c\ud55c \ub355\uc5d0 \ub4dc\ub514\uc5b4 \uc0c8 \ucc28\ub97c \ubf51\uc558\uc2b5\ub2c8\ub2e4! \uc2dc\uc6b4\uc804\uc73c\ub85c \uc77c\uc9c1\uc120 \ub3c4\ub85c\ub97c \ub530\ub77c \ucc28\ub97c \ud0c0\uace0 \ubaa9\uc801\uc9c0\ub85c \uc774\ub3d9\ud558\ub824 \ud569\ub2c8\ub2e4. \ubaa9\uc801\uc9c0\uae4c\uc9c0 \uac70\ub9ac\uac00 \uaf64 \ub418\uae30 \ub54c\ubb38\uc5d0, \uc911\uac04\uc911\uac04 \uc8fc\uc720\uc18c\uc5d0\uc11c \uc5f0\ub8cc\ub97c \ub123\uc73c\ub824\uace0 \ud569\ub2c8\ub2e4. \uc2dc\uc6b4\uc804 \uc911\uc5d0\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc870\uac74\uc744 \uc9c0\ucf1c\uc57c \ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$i$\ubc88\uc9f8 \uc8fc\uc720\uc18c\ub294 \uae38\uc758 \uc6d0\uc810\uc73c\ub85c\ubd80\ud130 \uc624\ub978\ucabd\uc73c\ub85c $x_{i}$\ud0ac\ub85c\ubbf8\ud130 \ub5a8\uc5b4\uc9c4 \uc704\uce58\uc5d0 \uc788\uc73c\uba70, \uc774 \uc8fc\uc720\uc18c\uc5d0\uc11c \ucc28\uc5d0 \ub123\uc744 \uc218 \uc788\ub294 \uc5f0\ub8cc\ub294 \ub9ac\ud130 \ub2f9 \ub2e8\uac00\uac00 $p_{i}$\uc774\uace0 \ucd1d $a_{i}$\ub9ac\ud130\ub9cc\ud07c\uc758 \uc5f0\ub8cc\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\r\n\t<li>\uc8fc\uc720\uc18c\uc5d0\uc11c\ub294 \uc5f0\ub8cc\ub97c $a_{i}$\ub9ac\ud130 \uc774\ud558\ub85c \uc6d0\ud558\ub294 \ub9cc\ud07c \uc8fc\uc720\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\r\n\t<li>\uac01 \uc8fc\uc720\uc18c\uc5d0\uc11c \uc8fc\uc720\ud55c \ub4a4 \ucc28\uc5d0 \ub4e4\uc5b4 \uc788\ub294 \uc5f0\ub8cc\uc758 \uc591\uc774 \ucc28\uc758 \uc5f0\ub8cc \uc6a9\ub7c9\uc778 $F$\ub9ac\ud130\ub97c \ub118\uaca8\uc11c\ub294 \uc548 \ub429\ub2c8\ub2e4.<\/li>\r\n\t<li>\ucc28\ub294 $1$\ub9ac\ud130\uc758 \uc5f0\ub8cc\ub85c $1$\ud0ac\ub85c\ubbf8\ud130\ub97c \uc6c0\uc9c1\uc77c \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\r\n\t<li>\uc0c8 \ucc28\ub294 \uc2dc\uc6b4\uc804 \uc804\uc5d0\ub294 \uc5f0\ub8cc\uac00 \uc5c6\uc2b5\ub2c8\ub2e4. \ub530\ub77c\uc11c \ucc28\uc758 \uc2dc\uc791 \uc9c0\uc810\uc740 \uccab \ubc88\uc9f8 \uc8fc\uc720\uc18c\uc785\ub2c8\ub2e4.<\/li>\r\n\t<li>\ubaa9\uc801\uc9c0\ub294 \uae38\uc758 \uc6d0\uc810\uc73c\ub85c\ubd80\ud130 \uc624\ub978\ucabd\uc73c\ub85c $X$\ud0ac\ub85c\ubbf8\ud130 \ub5a8\uc5b4\uc9c4 \uc704\uce58\uc785\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc740\ud558\ub294 \uc5f4\uc2ec\ud788 \ubc88 \ub3c8\uc744 \uc5f0\ub8cc\uc5d0 \uc4f0\ub294 \uac83\uc740 \uc544\uae4c\uc6cc, \ubaa9\uc801\uc9c0\uae4c\uc9c0 \ucd5c\uc18c \ube44\uc6a9\uc73c\ub85c \uc774\ub3d9\ud558\ub824 \ud569\ub2c8\ub2e4. \uc5ec\ub7ec\ubd84\uc740 \uc740\ud558\ub97c \ub3c4\uc640 \uc8fc\uc5b4\uc57c \ud569\ub2c8\ub2e4!<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uc8fc\uc720\uc18c\uc758 \uac1c\uc218 $N$, \ubaa9\ud45c \uc9c0\uc810 $X$ \ubc0f \ucc28\uc758 \uc5f0\ub8cc \uc6a9\ub7c9 $F$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(1\\leq N\\leq 500\\, 000;$ $1\\leq X,F\\leq 10^{9})$<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\ubd80\ud130 $N$\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uc8fc\uc720\uc18c\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \ubaa8\ub4e0 $1\\leq i\\leq N$\uc5d0 \ub300\ud574, $(i+1)$\ubc88\uc9f8 \uc904\uc5d0\ub294 $x_{i}$, $p_{i}$, $a_{i}$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(0\\leq x_{i}&lt;X$; $1\\leq p_{i}\\leq 10^{9}$; $1\\leq a_{i}\\leq F)$ \uac19\uc740 \uc704\uce58\uc5d0 \uc788\ub294 \uc8fc\uc720\uc18c\ub294 \uc5c6\uc73c\uba70, <strong>\uc8fc\uc720\uc18c\uc758 \uc704\uce58 $x_{i}$\ub294 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/strong> \uc989, \ubaa8\ub4e0 $2\\leq i\\leq N$\uc5d0 \ub300\ud574 $x_{i-1}&lt;x_{i}$\uc785\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uc5b4\ub5a4 \uacbd\ub85c\ub85c \uc2dc\uc6b4\uc804\uc744 \uc9c4\ud589\ud574\ub3c4 \ubaa9\uc801\uc9c0\uc5d0 \ub3c4\ub2ec\ud560 \uc218 \uc5c6\uc73c\uba74 \uccab\uc9f8 \uc904\uc5d0 <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4. \uadf8\ub807\uc9c0 \uc54a\uc73c\uba74 \uccab\uc9f8 \uc904\uc5d0 \uc2dc\uc6b4\uc804\uc744 \ub9c8\uce58\ub294 \ub370 \ub4dc\ub294 \ucd5c\uc18c \ube44\uc6a9\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"31398","problem_lang":"1","title":"Gas Station","description":"<p>Eunha has managed to buy a new car as a result of her hard work! For her test drive, she plans to drive along a straight road towards her destination. Since it&#39;s a long drive, she is going to stop at some gas stations on the way to refuel. The following conditions must be satisfied through the test drive.<\/p>\r\n\r\n<ul>\r\n\t<li>The $i$-th gas station is $x_{i}$ kilometers away to the right from the origin. Refueling at this station costs $p_{i}$ per liter of fuel, and there is a total of $a_{i}$ liters of fuel at the station.<\/li>\r\n\t<li>You may refuel as much as you want at a gas station up to $a_{i}$ liters.<\/li>\r\n\t<li>The total amount of fuel in the car after refueling must not exceed the car&#39;s capacity $F$.<\/li>\r\n\t<li>The car can travel $1$ kilometer using $1$ liter of fuel.<\/li>\r\n\t<li>The car has no fuel at the start of the test drive. Thus, the starting point of the drive is the first gas station.<\/li>\r\n\t<li>The destination is $X$ kilometers away to the right from the origin of the road.<\/li>\r\n<\/ul>\r\n\r\n<p>Eunha finds it a waste to spend her precious money on fuel and thus wishes to travel to her destination with minimum cost. It&#39;s your task to help Eunha!<\/p>\r\n","input":"<p>The first line of input contains three space-separated integers $N$, denoting the number of gas stations, $X$, denoting the destination point, and $F$, denoting the car&#39;s fuel capacity. $(1\\leq N\\leq 500\\, 000;$ $1\\leq X,F\\leq 10^{9})$<\/p>\r\n\r\n<p>Each of the next $N$ lines of input contains information about a gas station. For all $i$ such that $1\\leq i\\leq N$, the $(i+1)$-th line of input contains $x_{i}$, $p_{i}$, and $a_{i}$ separated by spaces. $(0\\leq x_{i}&lt;X$; $1\\leq p_{i}\\leq 10^{9}$; $1\\leq a_{i}\\leq F)$ No two gas stations are at the same location, and the <strong>locations are given in ascending order of $x_{i}$. <\/strong>That is, for all $2\\leq i\\leq N$, $x_{i-1}&lt;x_{i}$.<\/p>\r\n","output":"<p>If there is no route that allows Eunha to arrive at her destination, print <span style=\"color:#e74c3c;\"><code>-1<\/code><\/span>&nbsp;in the first line. Otherwise, print the minimum cost required to complete the test drive.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]