Problem: 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 [pl, pr] and Vasya chooses an integer v from the interval [vl, vr] (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 pl, pr, vl, vr and k (1 ≤ pl ≤ pr ≤ 109, 1 ≤ vl ≤ vr ≤ 109, 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, <image>

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.

Solution (in PYTHON):

Solution:
(pl, pr, vl, vr, k) = map(int, raw_input().split())

N = 10**9
def doit(n, res):
	if n > N: return
	res.append(n)
	doit(n * 10 + 4, res)
	doit(n * 10 + 7, res)
	return res

intersect = lambda l, r, pl, pr: max(0, (min(r, pr) - max(l, pl) + 1.0) / (pr - pl + 1))
nums = sorted(doit(0, []))
res = 0
for i in xrange(len(nums) - k + 1):
	a = (nums[i - 1] + 1) if i > 0 else 1
	b = nums[i]
	c = nums[i + k - 1]
	d = nums[i + k] - 1 if i + k < len(nums) else N
	res += intersect(a, b, pl, pr) * intersect(c, d, vl, vr)
	res += intersect(a, b, vl, vr) * intersect(c, d, pl, pr)
	if k == 1 and pl <= b <= pr and vl <= b <= vr: res -= 1.0 / (pr - pl + 1) / (vr - vl + 1)
print "%.9f" % res