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 <class T>
void pv(T a, T b) {
  for (T i = a; i != b; ++i) cerr << *i << ' ';
  cout << endl;
}
const int MAX_N = 1000000000;
vector<int> luckey;
void rec(long long cur) {
  if (cur > MAX_N) return;
  if (cur) luckey.push_back(cur);
  rec(cur * 10 + 4);
  rec(cur * 10 + 7);
}
long long overlap(long long a, long long b, long long c, long long d) {
  if (a > c) return overlap(c, d, a, b);
  if (b < c) return 0;
  return min(b, d) - c + 1;
}
int main() {
  rec(0);
  luckey.push_back(0);
  luckey.push_back(MAX_N + 1);
  sort((luckey).begin(), (luckey).end());
  long long pl, pr, vl, vr, k;
  cin >> pl >> pr >> vl >> vr >> k;
  long long hit = 0;
  long long total = (pr - pl + 1) * (vr - vl + 1);
  for (int i = 1; i + k < luckey.size(); i++) {
    long long add = 0;
    add += overlap(luckey[i - 1] + 1, luckey[i], pl, pr) *
           overlap(luckey[i + k - 1], luckey[i + k] - 1, vl, vr);
    add += overlap(luckey[i - 1] + 1, luckey[i], vl, vr) *
           overlap(luckey[i + k - 1], luckey[i + k] - 1, pl, pr);
    if (k == 1 && add > 0 && pl <= luckey[i] && luckey[i] <= pr &&
        vl <= luckey[i] && luckey[i] <= vr)
      add--;
    hit += add;
  }
  printf("%.10f\n", (double)hit / total);
  return 0;
}