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> l;
long long mini, maxi;
long long cur;
void rec(long long cur) {
  if (cur <= maxi) {
    if (cur >= mini) l.push_back(cur);
  } else
    return;
  rec(cur * 10 + 4);
  rec(cur * 10 + 7);
}
void genLucky(int a, int b) {
  mini = a;
  maxi = b;
  l.clear();
  rec(0);
  l.push_back(a - 1);
  l.push_back(b + 1);
  sort(l.begin(), l.end());
}
long double prob(int pa, int pb, int ia, int ib) {
  int s = max(pa, ia);
  int e = min(pb, ib);
  if (s > e) return 0.0;
  long double res = e - s + 1.0;
  res /= (ib - ia + 1);
  return res;
}
int main() {
  int i, j;
  int pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  genLucky(min(pl, vl), max(pr, vr));
  long double res = 0.0;
  if (k == 1) {
    for (i = 0; i + 2 < l.size(); ++i) {
      res += prob(l[i] + 1, l[i + 1], pl, pr) *
             prob(l[i + k] + 1, l[i + k + 1] - 1, vl, vr);
      res += prob(l[i] + 1, l[i + 1] - 1, pl, pr) *
             prob(l[i + k], l[i + k], vl, vr);
      res += prob(l[i] + 1, l[i + 1], vl, vr) *
             prob(l[i + k] + 1, l[i + k + 1] - 1, pl, pr);
      res += prob(l[i] + 1, l[i + 1] - 1, vl, vr) *
             prob(l[i + k], l[i + k], pl, pr);
      res +=
          prob(l[i + 1], l[i + 1], pl, pr) * prob(l[i + 1], l[i + 1], vl, vr);
    }
  } else {
    for (i = 0; i + k + 1 < l.size(); ++i) {
      res += prob(l[i] + 1, l[i + 1], pl, pr) *
             prob(l[i + k], l[i + k + 1] - 1, vl, vr);
      res += prob(l[i] + 1, l[i + 1], vl, vr) *
             prob(l[i + k], l[i + k + 1] - 1, pl, pr);
    }
  }
  printf("%.12lf\n", (double)res);
  return 0;
}