109_B. Lucky Probability
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.
```python
import itertools as it



all_lucky = []

for length in range(1, 10):
    for comb in it.product(['7', '4'], repeat=length):
        all_lucky += [int(''.join(comb))]

all_lucky.sort()

# print(len(all_lucky))

pl, pr, vl, vr, k = map(int, input().split())

result = 0

def inters_len(a, b, c, d):
    a, b = sorted([a, b])
    c, d = sorted([c, d])
    return (max([a, c]), min([b, d]))

def check_for_intervals(pl, pr, vl, vr):
    global result
    for i in range(1, len(all_lucky) - k):
        le, re = i, i + k - 1

        a, b = inters_len(all_lucky[le - 1] + 1, all_lucky[le], pl, pr)
        left_len = max([0, b - a + 1])
        c, d = inters_len(all_lucky[re], all_lucky[re + 1] - 1, vl, vr)
        right_len = max([0, d - c + 1])

        result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))

        if b == c and left_len * right_len > 1e-6:
            result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2


    a, b = inters_len(0, all_lucky[0], pl, pr)
    left_len = max([0, b - a + 1])
    c, d = inters_len(all_lucky[k - 1], all_lucky[k] - 1, vl, vr)
    right_len = max([0, d - c + 1])

    #print((left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)))
    #print(left_len, right_len)
    result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))

    if b == c and left_len * right_len > 1e-6:
        result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2

    a, b = inters_len(all_lucky[-(k + 1)] + 1, all_lucky[-k], pl, pr)
    left_len = max([0, b - a + 1])
    c, d = inters_len(all_lucky[-1], 10**9, vl, vr)
    right_len = max([0, d - c + 1])

    #print((left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1)))
    result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))

    if b == c and left_len * right_len > 1e-6:
        result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2



#print(all_lucky[:5])

if k != len(all_lucky):
    check_for_intervals(pl, pr, vl, vr)
    check_for_intervals(vl, vr, pl, pr)
else:
    a, b = inters_len(0, all_lucky[0], pl, pr)
    left_len = max([0, b - a + 1])
    c, d = inters_len(all_lucky[-1], 10**9, vl, vr)
    right_len = max([0, d - c + 1])
    result += (left_len / (pr - pl + 1)) * (right_len / (vr - vl + 1))

    if b == c and left_len * right_len > 1e-6:
        result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2

    a, b = inters_len(0, all_lucky[0], vl, vr)
    left_len = max([0, b - a + 1])
    c, d = inters_len(all_lucky[-1], 10**9, pl, pr)
    right_len = max([0, d - c + 1])
    result += (left_len / (vr - vl + 1)) * (right_len / (pr - pl + 1))

    if b == c and left_len * right_len > 1e-6:
        result -= (1 / (pr - pl + 1) / (vr - vl + 1)) / 2

print(result)




# Made By Mostafa_Khaled
```