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.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskB {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int pl = in.nextInt(), pr = in.nextInt(), vl = in.nextInt(), vr = in.nextInt(), k = in.nextInt();
            int[] lucky = genLucky();
            double ans = 0;
            for (int i = 1; i + k < 1024; ++i) {
                int xl = lucky[i - 1] + 1;
                int xr = lucky[i];
                int yl = lucky[i + k - 1];
                int yr = lucky[i + k] - 1;
                ans += prob(xl, xr, pl, pr) * prob(yl, yr, vl, vr);
                ans += prob(yl, yr, pl, pr) * prob(xl, xr, vl, vr);
                if (k == 1) {
                    ans -= prob(xr, xr, pl, pr) * prob(xr, xr, vl, vr);
                }
            }
            out.println(ans);
        }

        int[] genLucky() {
            int[] c = new int[1024];
            for (int len = 1, k = 1; len <= 9; ++len) {
                for (int msk = 0; msk < 1 << len; ++msk) {
                    int a = 0;
                    for (int j = 0, b = msk, f = 1; j < len; ++j, b >>= 1, f *= 10) {
                        if ((b & 1) == 0) {
                            a += f * 4;
                        } else {
                            a += f * 7;
                        }
                    }
                    c[k++] = a;
                }
            }
            c[c.length - 1] = (int) (2e9);
            return c;
        }

        double prob(int x, int y, int l, int r) {
            if (x < l) x = l;
            if (y > r) y = r;
            if (x > y) return 0;
            return 1.0 * (y - x + 1) / (r - l + 1);
        }

    }

    static class InputReader {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private void fillTokenizer() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            fillTokenizer();
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}