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;
int main() {
  double pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  vector<int> number;
  int size = 1022, max_num = 777777777;
  number.reserve(size);
  number.push_back(4);
  number.push_back(7);
  int index = 0;
  while (number.back() < max_num) {
    number.push_back(number[index] * 10 + 4);
    number.push_back(number[index] * 10 + 7);
    ++index;
  }
  double ans = 0;
  int start = 0, end = 1000000000;
  for (int l = 0, r = k - 1; r < size; ++l, ++r) {
    double xl, xr, yl, yr;
    if (l <= 0) {
      xl = start;
    } else {
      xl = number[l - 1] + 1;
    }
    xr = number[l];
    yl = number[r];
    if (r >= size - 1) {
      yr = end;
    } else {
      yr = number[r + 1] - 1;
    }
    xl = max(xl, pl);
    xr = min(xr, pr);
    yl = max(yl, vl);
    yr = min(yr, vr);
    if (xl <= xr && yl <= yr) {
      ans += ((xr - xl + 1) / (pr - pl + 1)) * ((yr - yl + 1) / (vr - vl + 1));
    }
    if (l <= 0) {
      xl = start;
    } else {
      xl = number[l - 1] + 1;
    }
    xr = number[l];
    yl = number[r];
    if (r >= size - 1) {
      yr = end;
    } else {
      yr = number[r + 1] - 1;
    }
    xl = max(xl, vl);
    xr = min(xr, vr);
    yl = max(yl, pl);
    yr = min(yr, pr);
    if (xl <= xr && yl <= yr) {
      ans += ((xr - xl + 1) / (vr - vl + 1)) * ((yr - yl + 1) / (pr - pl + 1));
    }
    if (k == 1 && number[l] >= pl && number[l] <= pr && number[l] >= vl &&
        number[l] <= vr) {
      ans -= 1 / ((pr - pl + 1) * (vr - vl + 1));
    }
  }
  cout << setprecision(12) << ans << endl;
  return 0;
}