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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
vector<long long> nums;
void fill(long long num) {
  if (num > 4444444444LL) return;
  nums.push_back(num);
  fill(num * 10 + 4);
  fill(num * 10 + 7);
}
struct segment {
  long long left;
  long long right;
};
long long intersect(segment& s1, segment& s2) {
  long long l = max(s1.left, s2.left);
  long long r = min(s2.right, s1.right);
  if (l > r) return 0;
  return r - l + 1;
}
int main() {
  fill(0);
  sort(nums.begin(), nums.end());
  segment p, v;
  segment q;
  int k;
  cin >> p.left >> p.right >> v.left >> v.right >> k;
  q.left = max(p.left, v.left);
  q.right = min(p.right, v.right);
  bool use_q = q.left <= q.right;
  long long total = (p.right - p.left + 1) * (v.right - v.left + 1);
  long long exact = 0;
  for (int i = 1; i + k - 2 < nums.size(); ++i) {
    int l = i;
    int r = i + k - 1;
    segment left = {nums[i - 1] + 1, nums[i]};
    segment right = {nums[i + k - 1], nums[i + k] - 1};
    exact += intersect(left, p) * intersect(right, v);
    exact += intersect(right, p) * intersect(left, v);
    if (use_q && k == 1 && q.left <= nums[i] && q.right >= nums[i]) --exact;
  }
  cout << setprecision(12) << (double)exact / total;
  return 0;
}