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 long long MAX_ = 7e9;
vector<long long> data;
void dfs(long long num) {
  if (num < MAX_) {
    data.push_back(num);
    dfs(num * 10 + 4);
    dfs(num * 10 + 7);
  }
}
long long intersect(long long a, long long b, long long x, long long y) {
  long long left = max(a, x);
  long long right = min(b, y);
  return max(right - left + 1, 0LL);
}
int main() {
  dfs(0);
  sort(data.begin(), data.end());
  long long pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  long long counts = 0;
  for (int index = 1; index < data.size() - k + 1; ++index) {
    int left = index;
    int right = index + k - 1;
    long long ll = data[left - 1];
    long long rr = data[right + 1];
    long long m1 = intersect(pl, pr, ll + 1, data[left]);
    long long mm1 = intersect(vl, vr, data[right], rr - 1);
    counts += m1 * mm1;
    long long m2 = intersect(vl, vr, ll + 1, data[left]);
    long long mm2 = intersect(pl, pr, data[right], rr - 1);
    counts += m2 * mm2;
    if (k == 1 && m1 * mm1 && m2 * mm2) counts--;
  }
  double ans = counts * 1.0 / (pr - pl + 1) / (vr - vl + 1);
  cout << setprecision(12) << ans << endl;
  return 0;
}