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:
#!/usr/bin/env python

from collections import deque

Pl, Pr, Vl, Vr, k = map(int,raw_input().strip().split())

q = deque()
lucky = []
q.append(0)
lucky.append(0)
while (len(q)):
	front = q.popleft()
	x = front*10+4
	y = x+3
	if (x<=10000000000):
		q.append(x)
		lucky.append(x)
	if (y<=10000000000):
		q.append(y)
		lucky.append(y)
	
minl = min(Pl,Vl)
maxr = max(Pr,Vr)

mini = maxi = -1 
for i in xrange(len(lucky)):
	if lucky[i] >= minl:
		mini = i
		break

for i in xrange(len(lucky)-1,0,-1):
	if lucky[i] <= maxr:
		maxi = i
		break

def intersect(x1,y1,x2,y2): 
	if x1>y2 or x2>y1:
		return (1,0) 
	else:
		return (max(x1,x2),min(y1,y2))
	
res = 0.0
inv = 1.0/(Pr-Pl+1)/(Vr-Vl+1)
for i in xrange(mini,maxi-k+2):
	left = lucky[i]
	right = lucky[i+k-1]
	pl =  intersect(Pl, Pr,lucky[i-1]+1,lucky[i])
	pr = intersect(Pl, Pr, lucky[i+k-1], lucky[i+k]-1)
	vl = intersect(Vl,Vr, lucky[i-1]+1,lucky[i])
	vr = intersect(Vl, Vr, lucky[i+k-1], lucky[i+k]-1)
	s = (pl[1]-pl[0]+1)*(vr[1]-vr[0]+1) + (vl[1]-vl[0]+1)*(pr[1]-pr[0]+1)
	if (k == 1 and (pl[1] == vr[0] or pr[0] == vl[1])):
		s = s-1
	res += inv*s

print "%.9f"%res