Problem F
Marathon

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Konni is just about to run a marathon for the first time. He’s well prepared for it and has all the equipment he needs to achieve a good time. Among the things he has prepared is a water pouch that will make sure he can drink constantly throughout the run. He wants to achieve the best time possible, and thus he needs some help planning on which refilling station he should stop to fill his water pouch.

It takes $Y$ seconds to fill his water pouch no matter the amount that is already in the pouch, and the pouch can hold at most $X$ ml of liquid. Konni always remembers to fill his bag before he starts a marathon and for every metre that he runs, he will drink $1$ml of liquid. If Konni has no liquid left, he will need to jog until he gets more water.

Can you help Konni in finding the best time he can run the marathon if he chooses to stop at the refilling stations in the most optimal way?

As everyone knows a marathon is $42\, 195$ metres.

Input

The first line of input contains three integers, $0 \leq N \leq 1\, 000\, 000$ the amount of refilling stations, $0 \leq X \leq 10\, 000$ the size of the water pouch in ml, $0 \leq Y \leq 100$ how long it takes to fill the water pouch.

The next line contains two integers $1 \leq H \leq 10$, the speed Konni runs at in metres per second and $1 \leq S \leq H$, the speed Konni jogs at in metres per second.

Next will follow $N$ lines, each containing one integer, where line $i$ contains the position of refilling station number $i$ given in metres from the start.

Output

Print the shortest time possible for Konni given that he chooses the refilling stations in the most optimal way in the format of $hh:mm:ss$.

Scoring

1 1000 40
10 5
1000

02:17:59

5 500 20
8 3
100
800
1200
20000
30000

03:47:24