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:
//package codeforces;
import java.io.*;
import java.util.*;

public class cf88D
{
    static ArrayList<Long> nums;
    static long p1,p2,v1,v2; static int k;
    public static void main(String[]args) throws IOException
    {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer(in.readLine());
        p1=Integer.parseInt(st.nextToken());
        p2=Integer.parseInt(st.nextToken());
        v1=Integer.parseInt(st.nextToken());
        v2=Integer.parseInt(st.nextToken());
        k=Integer.parseInt(st.nextToken());

        long max = Math.max(p2,v2);
        nums = new ArrayList<Long>();
        Queue<Long> q = new LinkedList<Long>();
        q.offer(0L);
        while(!q.isEmpty()) {
            long c = q.poll();
            nums.add(c);
            if(10*c+4<=max)
                q.offer(10*c+4);
            if(10*c+7<=max)
                q.offer(10*c+7);
        }
        nums.add(1000000001L);

        long sumValid=0;
        long sumTotal=(p2-p1+1L)*(v2-v1+1L);
        for (int i=1;i<=nums.size()-k-1;i++)
        {
            long a = nums.get(i);
            long b = nums.get(i+k-1);
            sumValid+=doIt(a,b,i,i+k-1);
        }
        System.out.printf("%.20f\n",(0.0+sumValid)/sumTotal);
    }

    public static long doIt(long a, long b, int ia,int ib)
    {
        Interval l1 = new Interval(nums.get(ia-1)+1,a),
             l2 = new Interval(b,nums.get(ib+1)-1),
             P1 = new Interval(p1,p2),
             V1 = new Interval(v1,v2);

        Interval r1 = l1.intersect(P1),
                 r2 = l2.intersect(V1),
                 r3 = l1.intersect(V1),
                 r4 = l2.intersect(P1);

        long ret = r1.getSize() * r2.getSize() + r3.getSize() * r4.getSize();

        if (k==1)
        {
            Interval t = new Interval(a, a);
            ret -= P1.intersect(t).getSize()*V1.intersect(t).getSize();
        }

        return  ret;

    }
}

class Interval
{
    long l,r;
    public Interval(long a, long b)
    {
        l=a;r=b;
    }

    boolean equals(Interval b)
    {
        return l==b.l && r==b.r;
    }
    public long getSize()
    {
        if (l==-1 || r<l) return 0;
        return r-l+1;
    }

    public Interval intersect(Interval b)
    {
        if (l<b.l && r<b.l || b.l<l && b.r<l) return new Interval(-1,-1);
        return new Interval(Math.max(l,b.l),Math.min(r,b.r));
    }

    public String toString()
    {
        return "["+l+", "+r+"]";
    }
}