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 ≤ 105) - 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 ≤ 105, 1 ≤ pm < pc ≤ 105) - 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 ≤ 105) - 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 ≤ 105) - 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.