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 PYTHON3):

Solution:
#!/usr/bin/env python3

import itertools

pl,pr,vl,vr,k = map(int, input().split())
l = min(pl, vl)
r = max(pr, vr)

# Generate all lucky numbers with the appropriate number of digits
# O(3**max_nr_digits) = O(3**9) < 20000
max_nr_digits = len(str(r))
lucky_numbers = []
for nr_digits in range(1,max_nr_digits+1):
  lucky_numbers.extend(int(''.join(i)) for i in itertools.product("47", repeat=nr_digits))

# Filter so we only have lucky numbers that can be in the intervals
lucky_numbers = [nr for nr in lucky_numbers if (l <= nr) and (nr <= r)]
lucky_numbers.sort()

if len(lucky_numbers) < k:
  print("%.12f" % 0.0)
  exit()

lucky_numbers.insert(0,l-1)
lucky_numbers.append(r+1)

total_pairs = (pr-pl+1) * (vr-vl+1)
good_pairs = 0
for start_index in range(len(lucky_numbers)-k-1):
  (a,b) = lucky_numbers[start_index], lucky_numbers[start_index+1]
  (c,d) = lucky_numbers[start_index+k], lucky_numbers[start_index+k+1]
  # A pair will have lucky_numbers[start_index+1 : start_index+1+k] in its interval when:
  # The smallest number of the pair is larger than a, but at most b
  # The largest number of the pair is at least c, but smaller than d
  good_pairs += max((min(b,pr)-max(a+1,pl)+1),0)*max((min(d-1,vr)-max(c,vl)+1),0)
  good_pairs += max((min(b,vr)-max(a+1,vl)+1),0)*max((min(d-1,pr)-max(c,pl)+1),0)
  if (b == c) and (pl <= b) and (b <= pr) and (vl <=b) and (b <= vr):
    # Prevent double counting of the pair (b,c) when b == c and both p and v can supply the value
    good_pairs -= 1

print("%.12f" % (good_pairs / total_pairs))