[failed] Life Transfer

Note: “feli” is the local currency. In the great city of Nekoresti, there are n people for which we know their ages: ai is the age of the i-th person. Currently, they are on vacation, so they decided to go on a trip to Pisiev to visit a Koshkseum, a famous museum. They can go either by car or by motorcycle:

• a car can transport k people (one driver which has to be at least lc years old and k - 1 passengers). The cost to rent a car is pc feli.

• a motorcycle can transport only one person (which has to be at least lm years old). The cost to rent a motorcycle is pm feli. Unfortunately, people have money issues, so they decided to consult Mewlin, the great local magician from the city. Using a formidable spell called Mucadabra, Mewlin can transfer age from one person to another. Formally, he can reduce the age x of a person and increase the age y of another person by the same amount (so the sum of ages is constant). The cost to transfer 1 unit of age is t feli. For magic medical reasons, the age of a person cannot be changed by more than d years (if the initial age is x, his age must be at least x - d and at most x + d at all times). Also, the age cannot go below 1 year old. Help the people from Nekoresti to spend as little money as possible, so they can arrive in Pisiev.

Input

The first line contains two integers n and k (1 <= n, k <= 10^5 ) — the number of people and the maximum number of people that can be in one car. The second line contains four integers lc , pc , lm and pm (1 <= lm < lc <= 10^5 , 1 <= pm < pc <= 10^5 ) — the minimum needed age to drive a car; the price of renting one car; the minimum needed age to drive a motorcycle and the price of renting one motorcycle. The third line contains two integers t and d (0 <= t, d <= 10^5 ) — the price of transferring one year and the maximum number of times the spells can be applied per each person. The fourth line contains n integers a1 , a2 , . . . , an (1 <= ai <= 10^5 ) — the age of the i-th person.

Output

Print one number, the smallest amount of feli the people need to spend in order for them to reach their destination. If there is no such solution, print -1.

Example 1

Input:

2 2
18 1000 16 1
5 3
16 15

Output:

1010

Example 2

Input:

2 2
23 10 15 5
2 2
9 20

Output:

-1