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.

Input

The single line contains five integers $*p*_{*l*}$, $*p*_{*r*}$, $*v*_{*l*}$, $*v*_{*r*}$ and $*k*$ ($1 ≤ *p*_{*l*} ≤ *p*_{*r*} ≤ 10^{9}, 1 ≤ *v*_{*l*} ≤ *v*_{*r*} ≤ 10^{9}, 1 ≤ *k* ≤ 1000$).

Output

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

Note

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.