Japan Alumni Group Summer Camp 2013 Warming Up

B - Cans of Toys


Time limit時間制限 : 1.5sec / Memory limitメモリ制限 : 96MB

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

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