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.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class B {

    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static PrintWriter out = new PrintWriter(System.out);
    
    static String nextToken() throws IOException{
        String s;
        while (st==null || !st.hasMoreTokens()){
            s = bf.readLine();
            if (s == null)
                return null;
            st = new StringTokenizer(s);
        }
        
        return st.nextToken();
    }
    
    static String nextStr() throws IOException{
        return nextToken();
    }
    
    static int nextInt() throws IOException{
        return Integer.parseInt(nextToken());
    }
    
    static long nextLong() throws IOException{
        return Long.parseLong(nextToken());
    }
    
    static double nextDouble() throws IOException{
        return Double.parseDouble(nextToken());
    }
    
    static int intersection(int l1, int r1, int l2, int r2){
        if (l1>=l2 && r1<=r2)
            return r1-l1+1;
        
        if (l2>=l1 && r2<=r1)
            return r2-l2+1;
        
        if (r1<l2 || l1>r2)
            return 0;
            
        if (l1<l2 && r1<r2)
            return r1-l2+1;
        
        if (l2<l1 && r2<r1)
            return r2-l1+1;
        
        return 0;
    }
    
    public static void main(String[] args) throws IOException{
        int pl = nextInt(),
            pr = nextInt(),
            vl = nextInt(),
            vr = nextInt(),
            k = nextInt();
        
        int a[] = new int[1024];
        int m = 1;
        
        for (int i=1; i<10; i++)
            for (int j=0; j<(1<<i); j++){
                int s = j;
                int n = 0;
                
                for (int t=0; t<i; t++){
                    if (s%2 == 0)
                        n = n*10+4;
                    else
                        n = n*10+7;
                    
                    s /= 2;
                }
                
                a[m++] = n;
            }
        
        a[m++] = 1000000001;
        
        Arrays.sort(a);
        
        double res = 0;

        for (int i=1; i<m-1; i++){
            int j = i+k-1;
            if (j >= m-1)
                break;
            
                if (k == 1){
                    res += intersection(a[i-1]+1, a[i]-1, pl, pr)/(pr-pl+1.0) * intersection(a[j]+1, a[j+1]-1, vl, vr)/(vr-vl+1.0);
                    if (a[i]>=pl && a[i]<=pr)
                        res += 1.0/(pr-pl+1.0)*intersection(a[j]+1, a[j+1]-1, vl, vr)/(vr-vl+1.0);
                    if (a[j]>=vl && a[j]<=vr)
                        res += 1.0/(vr-vl+1.0)*intersection(a[i-1]+1, a[i]-1, pl, pr)/(pr-pl+1.0);
                    
                    res += intersection(a[i-1]+1, a[i]-1, vl, vr)/(vr-vl+1.0) * intersection(a[j]+1, a[j+1]-1, pl, pr)/(pr-pl+1.0);
                    if (a[i]>=vl && a[i]<=vr)
                        res += 1.0/(vr-vl+1.0)*intersection(a[j]+1, a[j+1]-1, pl, pr)/(pr-pl+1.0);
                    if (a[j]>=pl && a[j]<=pr)
                        res += 1.0/(pr-pl+1.0)*intersection(a[i-1]+1, a[i]-1, vl, vr)/(vr-vl+1.0);
                    
                    if (a[j]>=vl && a[j]<=vr && a[i]>=pl && a[i]<=pr)
                        res += 1.0/(vr-vl+1.0)*1.0/(pr-pl+1.0);
                }
                else{
                    res += intersection(a[i-1]+1, a[i], pl, pr)/(pr-pl+1.0) * intersection(a[j], a[j+1]-1, vl, vr)/(vr-vl+1.0);
                    res += intersection(a[i-1]+1, a[i], vl, vr)/(vr-vl+1.0) * intersection(a[j], a[j+1]-1, pl, pr)/(pr-pl+1.0);
                }
            }
        
        out.println(res);
        out.flush();
    }

}