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31765번 - Activating Robots 다국어

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5 초 1024 MB148777.778%

문제

You and a single robot are initially at point 0ドル$ on a circle with perimeter $L$ (1ドル \le L \le 10^9$). You can move either counterclockwise or clockwise along the circle at 1ドル$ unit per second. All movement in this problem is continuous.

Your goal is to place exactly $R-1$ robots such that at the end, every two consecutive robots are spaced $L/R$ away from each other (2ドル\le R\le 20,ドル $R$ divides $L$). There are $N$ (1ドル\le N\le 10^5$) activation points, the $i$th of which is located $a_i$ distance counterclockwise from 0ドル$ (0ドル\le a_i<L$). If you are currently at an activation point, you can instantaneously place a robot at that point. All robots (including the original) move counterclockwise at a rate of 1ドル$ unit per $K$ seconds (1ドル\leq K\leq 10^6$).

Compute the minimum time required to achieve the goal.

입력

The first line contains $L,ドル $R,ドル $N,ドル and $K$.

The next line contains $N$ space-separated integers $a_1,a_2,\dots,a_N$.

출력

The minimum time required to achieve the goal.

제한

예제 입력 1

10 2 1 2
6

예제 출력 1

22

We can reach the activation point at 6ドル$ in 4ドル$ seconds by going clockwise. At this time, the initial robot will be located at 2ドル$. Wait an additional 18ドル$ seconds until the initial robot is located at 1ドル$. Now we can place a robot to immediately win.

예제 입력 2

10 2 1 2
7

예제 출력 2

4

We can reach the activation point at 7ドル$ in 3ドル$ seconds by going clockwise. At this time, the initial robot will be located at 1ドル.5$. Wait an additional second until the initial robot is located at 2ドル$. Now we can place a robot to immediately win.

예제 입력 3

32 4 5 2
0 23 12 5 11

예제 출력 3

48

예제 입력 4

24 3 1 2
16

예제 출력 4

48

힌트

출처

Olympiad > USA Computing Olympiad > 2023-2024 Season > USACO 2024 US Open Contest > Platinum 3번

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출처

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