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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class D {
    static ArrayList<Integer> a = new ArrayList<Integer>();

    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();
        int p1 = in.nextInt();
        int p2 = in.nextInt();
        int v1 = in.nextInt();
        int v2 = in.nextInt();
        int k = in.nextInt();
        genLucky(4);
        genLucky(7);
        Collections.sort(a);
        double res = 0;
        long pb, vb, pa, va, s, e, ss, ee;
        for (int i = 0; i + k - 1 < a.size(); i++) {
            pb = vb = pa = va = 0;

            s = a.get(i);
            if (i == 0)
                ss = 0;
            else
                ss = a.get(i - 1) + 1;

            e = a.get(i + k - 1);
            if (i + k - 1 == a.size() - 1)
                ee = 1000000001;
            else
                ee = a.get(i + k) - 1;

            if (p1 <= s)
                pb = Math.min(p2, s) - Math.max(p1, ss) + 1;
            if (v1 <= s)
                vb = Math.min(v2, s) - Math.max(v1, ss) + 1;
            if (p2 >= e)
                pa = Math.min(p2, ee) - Math.max(p1, e) + 1;
            if (v2 >= e)
                va = Math.min(v2, ee) - Math.max(v1, e) + 1;

            pa = Math.max(pa, 0);
            va = Math.max(va, 0);
            pb = Math.max(pb, 0);
            vb = Math.max(vb, 0);

            if (k != 1)
                res += pa * vb + pb * va;
            else {
                if(p1 <= s && s <= p2 && s <= v2 && s >= v1)
//              if (pa*va*pb*vb > 0)
                    res += pa * vb + pb * va - 1;
                else
                    res += pa * vb + pb * va;
            }
        }
        System.out.println(res / ((p2 - p1 + 1) * 1.0 * (v2 - v1 + 1)));
    }

    public static void genLucky(long r) {
        if (r > 1000000000)
            return;
        a.add((int) r);
        genLucky(r * 10 + 4);
        genLucky(r * 10 + 7);
    }

    // 1 20 100 120 5
    static class InputReader {
        BufferedReader in;
        StringTokenizer st;

        public InputReader() throws IOException {
            in = new BufferedReader(new InputStreamReader(System.in));
            st = new StringTokenizer(in.readLine());
        }

        public String next() throws IOException {
            while (!st.hasMoreElements())
                st = new StringTokenizer(in.readLine());
            return st.nextToken();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }
}