A8198. Lucky Probability

Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer $p$ from the interval $[p_{l},p_{r}]$ and Vasya chooses an integer $v$ from the interval $[v_{l},v_{r}]$ (also randomly). Both players choose their integers equiprobably. Find the probability that the interval $[min(v,p),max(v,p)]$ contains exactly $k$ lucky numbers.

The single line contains five integers $p_{l}$ , $p_{r}$ , $v_{l}$ , $v_{r}$ and $k$ ( $1<=p_{l}<=p_{r}<=10^{9},1<=v_{l}<=v_{r}<=10^{9},1<=k<=1000$ ).

On the single line print the result with an absolute error of no more than $10^{-9}$ .

Consider that $[a,b]$ denotes an interval of integers; this interval includes the boundaries. That is, 

In first case there are $32$ suitable pairs: $(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(7,1),(7,2),(7,3),(7,4),(8,1),(8,2),(8,3),(8,4),(9,1),(9,2),(9,3),(9,4),(10,1),(10,2),(10,3),(10,4)$ . Total number of possible pairs is $10·10=100$ , so answer is $32/100$ .

In second case Petya always get number less than Vasya and the only lucky $7$ is between this numbers, so there will be always $1$ lucky number.