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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Vector;
import java.util.Scanner;
import java.util.Collections;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author islammohsen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        Vector<Integer> vec = new Vector<>();

        void generate(long number) {
            if (number > (long) 1e9)
                return;
            vec.add((int) number);
            generate(number * 10 + 4);
            generate(number * 10 + 7);
        }

        int length(int l, int r) {
            if (l > r)
                return 0;
            return r - l + 1;
        }

        int intersect(int l1, int r1, int l2, int r2) {
            int l = Math.max(l1, l2);
            int r = Math.min(r1, r2);
            return length(l, r);
        }

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int pl = in.nextInt(), pr = in.nextInt(), vl = in.nextInt(), vr = in.nextInt(), k = in.nextInt();
            generate(4);
            generate(7);
            Collections.sort(vec);
            double ans = 0;
            for (int i = k - 1; i < vec.size(); i++) {
                int bfl, bfr, afl, afr, idx = i - k + 1;
                bfr = vec.elementAt(idx);
                if (idx - 1 < 0)
                    bfl = 1;
                else
                    bfl = vec.elementAt(idx - 1) + 1;
                afl = vec.elementAt(i);
                if (i + 1 == vec.size())
                    afr = (int) 1e9;
                else
                    afr = vec.elementAt(i + 1) - 1;
                //first choice
                ans += ((double) intersect(bfl, bfr, pl, pr) / length(pl, pr))
                        * ((double) intersect(afl, afr, vl, vr) / length(vl, vr));
                //second choice
                ans += ((double) intersect(bfl, bfr, vl, vr) / length(vl, vr))
                        * ((double) intersect(afl, afr, pl, pr) / length(pl, pr));
                if (k == 1)
                    ans -= ((double) intersect(vec.elementAt(i), vec.elementAt(i), pl, pr) / length(pl, pr))
                            * ((double) intersect(vec.elementAt(i), vec.elementAt(i), vl, vr) / length(vl, vr));
            }
            out.printf("%.12f", ans);
        }

    }
}