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<int> numbers;
double ver(int a, int b, int x, int y) {
  x = max(x, a);
  y = min(b, y);
  if (y < x) return 0;
  return static_cast<double>(y - x + 1) / (b - a + 1);
}
int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  int k;
  cin >> k;
  set<int> s;
  for (int len = 1; len <= 9; len++) {
    for (int i = 1; i <= 1024; i++) {
      int number = 0;
      for (int u = 0; u < len; u++) {
        if (i & (1 << u)) {
          number = number * 10 + 4;
        } else {
          number = number * 10 + 7;
        }
      }
      s.insert(number);
    }
  }
  s.insert(0);
  numbers.assign(s.begin(), s.end());
  numbers.push_back(1000000001);
  double ans = 0;
  for (int i = 1; i < numbers.size(); i++) {
    double g, h;
    if (i + k < numbers.size()) {
      g = ver(a, b, numbers[i - 1] + 1, numbers[i] - 1);
      h = ver(c, d, numbers[i + k - 1], numbers[i + k] - 1);
      ans += g * h;
      if (i != numbers.size()) {
        g = ver(a, b, numbers[i], numbers[i]);
        h = ver(c, d, numbers[i + k - 1], numbers[i + k] - 1);
        ans += g * h;
      }
    }
    if (i - k - 1 >= 0) {
      g = ver(a, b, numbers[i - 1] + 1, numbers[i] - 1);
      h = ver(c, d, numbers[i - k - 1] + 1, numbers[i - k]);
      ans += g * h;
    }
    if (i - k >= 0) {
      if (i != numbers.size()) {
        g = ver(a, b, numbers[i], numbers[i]);
        int tp = numbers[i - k + 1];
        if (i + k - 1 < numbers.size() && numbers[i + k - 1] == tp) --tp;
        h = ver(c, d, numbers[i - k] + 1, tp);
        ans += g * h;
      }
    }
  }
  cout << fixed << setprecision(10) << ans << endl;
  return 0;
}