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(n, cur):
    if n == 0:
        global arr
        arr.append(cur)
    else:
        gen(n - 1, cur + '4')
        gen(n - 1, cur + '7')

def lseg(x1, x2):
    if x2 < x1:
        return 0
    return x2 - x1 + 1

def inter2(x1, x2, a, b):
    left = max(x1, a)
    right = min(x2, b)
    return (left, right)

def inter(x1, x2, a, b):
    l, r = inter2(x1, x2, a, b)
    return lseg(l, r)

def minus(a, b, c, d):
    d1 = (-1, c - 1)
    d2 = (d + 1, 10 ** 10)
    d1 = inter(a, b, *d1)
    d2 = inter(a, b, *d2)
    return d1 + d2

arr = []
for i in range(1, 11):
    gen(i, '')
arr = [0] + sorted(list(map(int, arr)))

pl, pr, vl, vr, k = map(int, input().split())
ans = 0

for start in range(1, len(arr) - k + 1):
    if arr[start + k - 1] > max(vr, pr):
        break
    if arr[start] < min(pl, vl):
        continue
    goleft = inter(pl, pr, arr[start - 1] + 1, arr[start])
    goright = inter(vl, vr, arr[start + k - 1], arr[start + k] - 1)
    left, right = inter2(pl, pr, arr[start - 1] + 1, arr[start]), \
            inter2(vl, vr, arr[start + k - 1], arr[start + k] - 1)
    ans += goleft * goright

    left1 = inter2(pl, pr, arr[start + k - 1], arr[start + k] - 1)
    right1 = inter2(vl, vr, arr[start - 1] + 1, arr[start])

    ans += minus(right1[0], right1[1], right[0], right[1]) * lseg(*left1)
    ans += (lseg(*right1) - minus(right1[0], right1[1], right[0], right[1])) \
            * minus(left1[0], left1[1], left[0], left[1])


ans /= (pr - pl + 1) * (vr - vl + 1)
print(ans)