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 static java.util.Arrays.*;
import static java.lang.Math.*;
import static java.math.BigInteger.*;
import java.util.*;
import java.math.*;
import java.io.*;

public class B implements Runnable
{
    String file = "input";
    
    boolean TEST = false;
    
    int MAX = (int)(1e9);
    List<Integer> list;
    
    void solve() throws IOException
    {
        list = new ArrayList<Integer>();
        get(0);
        Integer[] a = list.toArray(new Integer[0]);
        sort(a);
        //print(a);
        long p1 = nextInt(), p2 = nextInt(), q1 = nextInt(), q2 = nextInt();
        int k = nextInt();
        long num = 0;
        for(int i = 0; i + k - 1 < a.length; i++)
        {
            long x = a[i], y = a[i + k - 1];
            long px = i > 0 ? a[i - 1] : 0;
            long ay = i + k < a.length ? a[i + k] : 1 << 30;
            long tmp = calc(p1, p2, px + 1, x) * calc(q1, q2, y, ay - 1) + calc(p1, p2, y, ay - 1) * calc(q1, q2, px + 1, x);
            if(k == 1 && p1 <= x && x <= p2 && q1 <= y && y <= q2) tmp--;
            num += tmp;
        }
        long total = (p2 - p1 + 1) * (q2 - q1 + 1);
        double res = (double)num / total;
        out.printf("%.12f\n", res);
    }
    
    long calc(long p1, long p2, long a, long b)
    {
        long L = max(p1, a);
        long R = min(p2, b);
        if(R >= L) return R - L + 1;
        return 0;
    }
    
    void get(long x)
    {
        if(x > MAX) return;
        if(x > 0) list.add((int)x);
        get(x * 10 + 4);
        get(x * 10 + 7);
    }
    
    String next() throws IOException
    {
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(input.readLine());
        return st.nextToken();
    }
    
    int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }
    
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    
    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    
    void print(Object... o)
    {
        System.out.println(deepToString(o));
    }
    
    void gcj(Object o)
    {
        String s = String.valueOf(o);
        out.println("Case #" + test + ": " + s);
        System.out.println("Case #" + test + ": " + s);
    }
    
    BufferedReader input;
    PrintWriter out;
    StringTokenizer st;
    int test;
    
    void init() throws IOException
    {
        if(TEST) input = new BufferedReader(new FileReader(file + ".in")); 
        else input = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }
    
    public static void main(String[] args) throws IOException
    {
        new Thread(null, new B(), "", 1 << 20).start();
    }
    
    public void run()
    {
        try
        {
            init();
            if(TEST) 
            {
                int runs = nextInt();
                for(int i = 0; i < runs; i++) solve();
            }
            else solve();
            out.close();        
        }
        catch(Exception e)
        {
            e.printStackTrace();
            System.exit(1);
        }
    }
}