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D. Lucky Probability

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya 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}.

Examples

Input

1 10 1 10 2

Output

0.320000000000

Input

5 6 8 10 1

Output

1.000000000000

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.

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