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.util.ArrayList;
import java.util.Collections;

/**
 * Created by IntelliJ IDEA.
 * User: piyushd
 * Date: 3/26/11
 * Time: 10:53 PM
 * To change this template use File | Settings | File Templates.
 */


public class TaskB {

    final int LIMIT = 123456789;
    ArrayList<Integer> lucky;

    void precal(int n) {
        lucky.add(n);
        if(n > LIMIT) return;
        precal(10 * n + 4);
        precal(10 * n + 7);
    }

    long solve(int l1, int r1, int l2, int r2, int k) {
        long ret = 0;

        for(int i = 0; i + k - 1 < lucky.size(); i++) {
            int j = i + k - 1;
            int x1 = l1, y1 = r1, x2 = l2, y2 = r2;

            if(i > 0) x1 = Math.max(l1, lucky.get(i - 1) + 1);
            y1 = Math.min(r1, lucky.get(i));
            x2 = Math.max(l2, lucky.get(j));
            if(j + 1 < lucky.size()) y2 = Math.min(r2, lucky.get(j + 1) - 1);

            if(y1 >= x1 && y2 >= x2) ret += (y1 - x1 + 1) * (long)(y2 - x2 + 1);
        }

        return ret;
    }

    void run() {
        int pl = nextInt(), pr = nextInt();
        int vl = nextInt(), vr = nextInt();
        int k = nextInt();

        this.lucky = new ArrayList<Integer>();
        precal(4);
        precal(7);
        Collections.sort(lucky);

        long totalWays = (pr - pl + 1) * (long) (vr - vl + 1);
        long ways = solve(pl, pr, vl, vr, k);
        ways += solve(vl, vr, pl, pr, k);
        if(k == 1) {
            for(int x : lucky)
                if(x >= vl && x <= vr && x >= pl && x <= pr)
                    ways--;
        }

        System.out.println((ways * 1.0) / totalWays);
    }

    int nextInt() {
        try {
            int c = System.in.read();
            if (c == -1) return c;
            while (c != '-' && (c < '0' || '9' < c)) {
                c = System.in.read();
                if (c == -1) return c;
            }
            if (c == '-') return -nextInt();
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = System.in.read();
            } while ('0' <= c && c <= '9');
            return res;
        } catch (Exception e) {
            return -1;
        }
    }

    long nextLong() {
        try {
            int c = System.in.read();
            if (c == -1) return -1;
            while (c != '-' && (c < '0' || '9' < c)) {
                c = System.in.read();
                if (c == -1) return -1;
            }
            if (c == '-') return -nextLong();
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = System.in.read();
            } while ('0' <= c && c <= '9');
            return res;
        } catch (Exception e) {
            return -1;
        }
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String next() {
        try {
            StringBuilder res = new StringBuilder("");
            int c = System.in.read();
            while (Character.isWhitespace(c))
                c = System.in.read();
            do {
                res.append((char) c);
            } while (!Character.isWhitespace(c = System.in.read()));
            return res.toString();
        } catch (Exception e) {
            return null;
        }
    }

    String nextLine() {
        try {
            StringBuilder res = new StringBuilder("");
            int c = System.in.read();
            while (c == '\r' || c == '\n')
                c = System.in.read();
            do {
                res.append((char) c);
                c = System.in.read();
            } while (c != '\r' && c != '\n');
            return res.toString();
        } catch (Exception e) {
            return null;
        }
    }

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