B - Cans of Toys
Editorial
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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

It is known that a gold angel is printed in probability

In addition, it is rumored that there is a rainbow angel which appears when you are really lucky. In this case, you can get

Calculate the expected number of Chocoball packages one needs to buy to get at least

The input file contains three real numbers

It is guaranteed that the expected value is lower than

Output the expected value as a decimal fraction.

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

Time Limit: 1.5 sec / Memory Limit: 93 MB

### Description

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

`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

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