Source: Mediamania.de
First Orchard is a cooperative game for children 2 years and
up. In this simple game, the players pick colored fruits from
trees in an orchard and place them into a basket. To make the
game more interesting, a raven tries to reach the orchard to
steal the fruits. If the players are successful in moving all
fruits into the basket before the raven can get to the orchard,
they’ll win. If the raven gets there first, the players
lose!
Your task is to determine the probability with which the
players will win!
The game is played as follows. There are $4$ trees in the orchard, each bearing
a different type of fruit: red apples, green apples, blue
plums, and yellow pears. The raven tries to reach the orchard
through a pathway containing one or more steps.
At each turn, the players roll a sixsided die. Four of the
faces show a color (red, green, yellow, blue), the fifth face
shows a fruit basket, and the sixth face shows a raven. All six
faces can appear with equal probability.

Red, Green, Yellow,
Blue. In these cases, a fruit with the
corresponding color is placed into the basket, provided the
tree corresponding to this color still has any fruits left
to pick. Otherwise, the players move on to the next
turn.

Fruit Basket. If the players roll the ’basket’
face, they will pick a fruit from the tree that has the
largest number of fruits left. If there are multiple such
trees with the same number of fruits, any of the trees can
be chosen.

Raven. If the ’raven’ face appears on the die,
then the raven moves one step closer towards the
orchard.
The game is over if either the players have picked all
fruits, or if the raven reaches the orchard, whichever happens
first. If the raven reaches the orchard before the players have
placed all fruits into the basket, the players lose.
Input
The input consists of a single test case with a single line
of input. The input contains five integer numbers: $R$, $G$, $B$, $Y$ and $S$. The values of $R, G, B$ and $Y$ are the number of red, green,
blue, and yellow fruits initially on each tree, respectively,
and $S$ denotes the number
of steps on the raven’s pathway. Since the game is intended for
young children, there will be at most $4$ fruits of each color: $0 \le R, G, B, Y \le 4$. There will
be at least one fruit overall: $0
< R + G + B + Y$. The raven will require at least
$1$ and at most
$8$ steps: $1 \le S \le 8$. The number of steps
is equal to the number of times the raven must appear on the
die for the players to lose.
Output
Output the probability that the players will win as a
floating point number. The absolute error of your result should
be less than $10^{5}$.
Sample Input 1 
Sample Output 1 
1 1 0 0 3

0.920138888889

Sample Input 2 
Sample Output 2 
4 4 4 4 5

0.631357306601

Sample Input 3 
Sample Output 3 
4 4 4 4 4

0.459393713591
