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;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
int p1, p2, v1, v2, k;
vector<int> lucky;
double prob(int sm, int bg, int st, int dr) {
  if (sm > dr || bg < st) return 0;
  if (bg > dr) bg = dr;
  if (sm < st) sm = st;
  return 1.0 * (bg - sm + 1) / (dr - st + 1);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> p1 >> p2 >> v1 >> v2 >> k;
  int idx = 0;
  lucky.push_back(0);
  for (int i = 1; i <= 9; ++i) {
    int sz = lucky.size();
    for (int j = idx; j < sz; ++j)
      lucky.push_back(lucky[j] * 10 + 4), lucky.push_back(lucky[j] * 10 + 7);
    idx = sz;
  }
  lucky.push_back(1000000001);
  double answer = 0;
  for (int i = 1; i + k < lucky.size(); ++i) {
    answer += prob(lucky[i - 1] + 1, lucky[i], p1, p2) *
              prob(lucky[i + k - 1], lucky[i + k] - 1, v1, v2);
    answer += prob(lucky[i - 1] + 1, lucky[i], v1, v2) *
              prob(lucky[i + k - 1], lucky[i + k] - 1, p1, p2);
    if (k == 1) {
      answer -=
          prob(lucky[i], lucky[i], p1, p2) * prob(lucky[i], lucky[i], v1, v2);
    }
  }
  printf("%.12lf", answer);
  return 0;
}