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;
const double pi = acos(-1.0), eps = 1e-7;
const long long inf = (1 << (30));
const long long infL = ((1ll) << (62));
inline bool isEqual(const double& x, const double& y) {
  return fabs(x - y) < eps;
}
inline bool isLess(const double& x, const double& y) { return x < y - eps; }
inline bool isLE(const double& x, const double& y) { return x < y + eps; }
long long getCommon(long long s1, long long f1, long long s2, long long f2) {
  if (f1 < s2 || f2 < s1) return 0;
  return min(f1, f2) - max(s1, s2) + 1;
}
int main() {
  long long pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  vector<long long> lucky;
  for (long long I = 0; I < (10); I++) {
    long long n = I + 1;
    for (long long mask = 0; mask < (1 << n); mask++) {
      long long x = 0;
      for (long long K = 0; K < (n); K++)
        if ((mask >> K) & 1)
          x = x * 10 + 4;
        else
          x = x * 10 + 7;
      lucky.push_back(x);
    }
  }
  lucky.push_back(0);
  lucky.push_back((1 << 31) - 1);
  sort(lucky.begin(), lucky.end());
  long long p = 0;
  for (long long I = 1; I < (long long)lucky.size() - k; I++) {
    long long s1 = lucky[I - 1] + 1, f1 = lucky[I];
    long long s2 = lucky[I + k - 1], f2 = lucky[I + k] - 1;
    p += getCommon(s1, f1, pl, pr) * getCommon(s2, f2, vl, vr);
    p += getCommon(s2, f2, pl, pr) * getCommon(s1, f1, vl, vr);
    if (k == 1 && getCommon(lucky[I], lucky[I], pl, pr) &&
        getCommon(lucky[I], lucky[I], vl, vr))
      p--;
  }
  double answer = double(p) / ((long long)(pr - pl + 1) * (vr - vl + 1));
  cout << fixed << setprecision(12) << answer << endl;
  return 0;
}