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:
def gen_len(l):
    gen = []
    for i in range(2 ** l):
        k = int(bin(i)[2:].rjust(l, '0').replace('0', '4').replace('1', '7'))
        if k <= 10 ** 9:
            gen.append(k)
    return gen


def pairs_with_k_len(a, k):
    l = 0
    r = k - 1
    while r < len(a):
        yield l, r
        l += 1
        r += 1


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


def main():
    gen = set()
    for i in range(1, 10):
        for e in gen_len(i):
            gen.add(e)
    gen = list(sorted(gen))

    pl, pr, vl, vr, k = map(int, input().split())
    denominator = (pr - pl + 1) * (vr - vl + 1)
    p = (pl, pr)
    v = (vl, vr)

    count = 0
    for l, r in pairs_with_k_len(gen, k):
        if gen[l] >= min(pl, vl) and gen[r] <= max(pr, vr):
            l1 = gen[l - 1] if l != 0 else 0
            r1 = gen[l]
            l2 = gen[r]
            r2 = gen[r + 1] if r != len(gen) - 1 else 10**9 + 1
            count += (get_intersection_length(l1 + 1, r1, pl, pr)
                      * get_intersection_length(l2, r2 - 1, vl, vr))
            count += (get_intersection_length(l1 + 1, r1, vl, vr) *
                      get_intersection_length(l2, r2 - 1, pl, pr))
            if k == 1 and get_intersection_length(vl, vr, pl, pr) != 0:
                count -= 1

    print(f"{(count / denominator):.{12}f}")


if __name__ == '__main__':
    main()