### Description

Chocoball is a great snack, it is not only because it tastes good, but also because you can get Cans of Toys when you are lucky.

When an angel is printed inside a package of Chocoball, you are lucky. There are two types of angels: gold angels and silver angels. You can get a Can of Toys in exchange of `1` package with a gold angel or `N` packages with silver angels.

It is known that a gold angel is printed in probability `p` and a silver angel is printed in probability `q`. (Two or more angels are never printed in one package.)

In addition, it is rumored that there is a rainbow angel which appears when you are really lucky. In this case, you can get `K` Cans of Toys at once. It is rumored that a rainbow angel is printed in probability `r`.

Calculate the expected number of Chocoball packages one needs to buy to get at least `M` Cans of Toys.

### Input

The input file contains three real numbers `p`, `q` and `r` (`0 \leq p,q,r,p+q+r \leq 1`) followed by three integers `N`, `K` (`1 \leq N, K \leq 40`) and `M` (`1 \leq M \leq 10^9`)

It is guaranteed that the expected value is lower than `10^{12}`.

### Output

Output the expected value as a decimal fraction.

The value which is accurate to within a relative value of 1E-6 will be accepted.