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:
luck = []
N = 1000000001
def radio(l, r, al, ar):
        return max(0.0, 1.0 * (r - l + 1) / (ar - al + 1))
def get_res(pl, pr, vl, vr, k, hash_t):
        res = 0
        n = len(luck)
        for i in range(0, n - k - 1):
                bl, br = luck[i] + 1, luck[i + 1]
                el, er = luck[i + k], luck[i + k + 1] - 1
                vbl, vbr = max(bl, pl), min(br, pr)
                vel, ver = max(el, vl), min(er, vr)
                add = radio(vbl, vbr, pl, pr) * radio(vel, ver, vl, vr)
                if add != 0:
                    res += add
                    hash_t.append((vbl, vbr, vel, ver))
        return res
def build_luck(s):
        if s < N:
                luck.append(s)
                build_luck(s * 10 + 4)
                build_luck(s * 10 + 7)
build_luck(0)
luck.append(N)
luck.sort()
pl, pr, vl, vr, k = map(int, raw_input().split())
p_hash = []
v_hash = []
res = get_res(pl, pr, vl, vr, k, p_hash) + get_res(vl, vr, pl, pr, k, v_hash)
if k == 1:
    for i in p_hash:
        for j in v_hash:
            pll = max(i[0], j[2])
            prr = min(i[1], j[3])
            vll = max(i[2], j[0])
            vrr = min(i[3], j[1])
            add = radio(pll, prr, pl, pr) * radio(vll, vrr, vl, vr)
            if add != 0:
                res -= add
                break
print res