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:
import sys
def read_values():
  return map(int,raw_input().split())

pl,pr,vl,vr,k=read_values()
P=1.0*(pr-pl+1)
V=1.0*(vr-vl+1)
res=0.0
L = []
l = ['']
for i in range(10):
  n=len(l)
  nextl=[]
  for j in range(n):
    nextl.append('4'+l[j])
    nextl.append('7'+l[j])
  l = nextl
  L += l
L=map(int,L)
L.sort()
n=len(L)

for i in range(n):
  if i+k>n: break
  a = pl
  if i>0:
    a = max(pl, L[i-1]+1)
  b = min(pr, L[i])
  c = max(vl, L[i+k-1])
  d = vr
  if i+k<n:
    d = min(vr, L[i+k]-1)
  if a<=b and c<=d:
    res += (b-a+1)/P*(d-c+1)/V
    
  a = vl
  if i>0:
    a = max(vl, L[i-1]+1)
  b = min(vr, L[i])
  c = max(pl, L[i+k-1])
  d = pr
  if i+k<n:
    d = min(pr, L[i+k]-1)
  if a<=b and c<=d:
    res += (b-a+1)/P*(d-c+1)/V

if k==1:
  for i in range(n):
    if pl<=L[i]<=pr and vl<=L[i]<=vr:
      res -= 1.0/P/V

#res/=P*V

print res