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;
using li = long long;
using ld = long double;
using pii = pair<int, int>;
const int INF = 1e9 + 13;
const int M = 1e9 + 7;
const int N = 2e5 + 13;
const int A = 513;
int di[] = {0, 1, -1, 0};
int dj[] = {1, 0, 0, -1};
mt19937 rnd(0);
int inter(int l, int r, int lf, int rg) {
  return max(0, min(r, rg) - max(l, lf) + 1);
}
int main() {
  int al, ar, bl, br, k;
  cin >> al >> ar >> bl >> br >> k;
  vector<int> a;
  for (int i = 1; i <= 9; i++) {
    for (int mask = 0; mask < (1 << i); mask++) {
      int x = 0;
      int p = 1;
      for (int j = 0; j < i; j++) {
        if (mask & (1 << j))
          x += p * 4;
        else
          x += p * 7;
        p *= 10;
      }
      a.push_back(x);
    }
  }
  a.push_back(-1);
  a.push_back(INF);
  sort(a.begin(), a.end());
  ld ans = 0;
  for (int i = 1; i + k < a.size(); i++) {
    ans += ld(inter(a[i - 1] + 1, a[i], al, ar)) / (ar - al + 1) *
           ld(inter(a[i + k - 1], a[i + k] - 1, bl, br)) / (br - bl + 1);
    ans += ld(inter(a[i - 1] + 1, a[i], bl, br)) / (br - bl + 1) *
           ld(inter(a[i + k - 1], a[i + k] - 1, al, ar)) / (ar - al + 1);
    if (k == 1) {
      ans -= ld(inter(a[i], a[i], bl, br)) / (br - bl + 1) *
             ld(inter(a[i], a[i], al, ar)) / (ar - al + 1);
    }
  }
  cout << setprecision(20) << fixed << ans << endl;
}