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:
s = list()
def rec(x):
    if x > 100000000000:
        return
    s.append(x)
    rec(x * 10 + 4)
    rec(x * 10 + 7)


def f(l1, r1, l2, r2):
    l1 = max(l1, l2)
    r1 = min(r1, r2)
    return max(r1 - l1 + 1, 0)


def main():
    rec(0)
    s.sort()
    args = input().split()
    pl, pr, vl, vr, k = int(args[0]), int(args[1]), int(args[2]), int(args[3]), int(args[4])
    ans = 0
    i = 1
    while i + k < len(s):
        l1 = s[i - 1] + 1
        r1 = s[i]
        l2 = s[i + k - 1]
        r2 = s[i + k] - 1
        a = f(l1, r1, vl, vr) * f(l2, r2, pl, pr)
        b = f(l1, r1, pl, pr) * f(l2, r2, vl, vr)
        ans += a + b
        if k == 1 and a > 0 and b > 0:
            ans -= 1
        i += 1
    all = (pr - pl + 1) * (vr - vl + 1)
    print(1.0 * ans / all)


if __name__ == '__main__':
    main()