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.*;
import java.util.*;
import java.text.*;

public class Main {
    static int p2,v2,p1,v1;
    static int j=0;
    static int[] l1=new int[1000000];
    
    static long d(int a1,int b1,int a2,int b2) {
     int a=Math.max(a1,a2);
     int b=Math.min(b1,b2);
     if (b<a) return 0;
     return b-a+1;
    }
    
    static void dfs(int x) {
        if (x>Math.max(p2,v2)) return;
        if (x>=Math.min(p1,v1)) {j++;l1[j]=x;}
        if (x/100000000==0)  {dfs(x*10+7);
        dfs(x*10+4);}
    }
    
    public static void main(String[] args) {
       Scanner in=new Scanner(System.in);
        p1=in.nextInt();
        p2=in.nextInt();
        v1=in.nextInt();
        v2=in.nextInt();
       int k=in.nextInt();
       double n=0;
       dfs(4);
       dfs(7);
       int[] l=new int[j+2];
       for (int i=1;i<=j;i++) l[i]=l1[i];
       l[j+1]=1000000000;
       Arrays.sort(l);
       int g;
       
       if (p1>v1) 
       {
        g=p1; p1=v1; v1=g;
        g=p2; p2=v2; v2=g;
       }
       
      NumberFormat nf = NumberFormat.getInstance();
      nf.setMaximumFractionDigits(20);
      
       for (int a=1;a<=j-k+1;a++)
       {
           int b=a+k-1;
           n+=d(l[a-1]+1,l[a],p1,p2)*d(l[b],l[b+1]-1,v1,v2);
           n+=d(l[a-1]+1,l[a],v1,v2)*d(l[b],l[b+1]-1,p1,p2);
           if (a==b&d(l[a],l[a],v1,v2)>0&d(l[a],l[a],p1,p2)>0) n--;
       }
      n/=(p2-p1+1);
      n/=(v2-v1+1);
      if (n>1) n=1;
      System.out.println(nf.format(n));

    }
}