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 JAVA):

Solution:
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Locale;
import java.util.Scanner;

public class B implements Runnable {
    private Scanner in;
    private PrintWriter out;

    private final int MAX = 1000000000;

    private ArrayList<Integer> lucky;

    private void gen(long n) {
        if (n > MAX) {
            return;
        }
        lucky.add((int) n);
        gen(n * 10 + 4);
        gen(n * 10 + 7);
    }

    private void solve() {
        int lo1 = in.nextInt();
        int hi1 = in.nextInt();
        int lo2 = in.nextInt();
        int hi2 = in.nextInt();
        int k = in.nextInt();
        lucky = new ArrayList<Integer>();
        gen(4);
        gen(7);
        Collections.sort(lucky);
        long sum = 0;
        for (int i = 0; i + k - 1 < lucky.size(); ++i) {
            int to1 = lucky.get(i);
            int from1 = i == 0 ? 0 : lucky.get(i - 1) + 1;
            int from2 = lucky.get(i + k - 1);
            int to2 = i + k == lucky.size() ? MAX : lucky.get(i + k) - 1;
            int co = 0;
            if (from1 <= hi1 && to1 >= lo1 && from2 <= hi2 && to2 >= lo2) {
                sum += 1L * (Math.min(to1, hi1) - Math.max(from1, lo1) + 1)
                        * (Math.min(to2, hi2) - Math.max(from2, lo2) + 1);
                ++co;
            }
            if (from1 <= hi2 && to1 >= lo2 && from2 <= hi1 && to2 >= lo1) {
                sum += 1L * (Math.min(to1, hi2) - Math.max(from1, lo2) + 1)
                        * (Math.min(to2, hi1) - Math.max(from2, lo1) + 1);
                ++co;
            }
            if (k == 1 && co == 2) {
                --sum;
            }
        }
        double ans = 1. * sum / (1L * (hi1 - lo1 + 1) * (hi2 - lo2 + 1));
        out.printf("%.10f", ans);
    }

    @Override
    public void run() {
        Locale.setDefault(Locale.US);
        in = new Scanner(System.in);
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    public static void main(String[] args) {
        new B().run();
    }
}