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.

Sample Input

0.5 0 0
1 1 1

Sample Output

2.000000

Sample Input

0.5 0.5 0
2 1 1

Sample Output

1.500000

Sample Input

0.3 0.6 0.1
2 2 2

Sample Output

2.836000

Source Name

The First KMCMonthly Contest