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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class D {
	
	static ArrayList<Long> lucky;
	
	public static void main(String[] args) throws IOException{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		lucky = new ArrayList<>();
		lucky.add(0L); lucky.add(4L);
		for(int i = 1; i < 1025; i++)
			lucky.add(nxtLucky(lucky.get(i)));

		int l1 = sc.nextInt(), r1 = sc.nextInt(), l2 = sc.nextInt(), r2 = sc.nextInt(), k = sc.nextInt();
		int i = 0, j = k + 1;
		long ans = 0;
		while(j < lucky.size())
		{
			ans += intersect(l1, r1, lucky.get(i) + 1, lucky.get(i + 1)) * intersect(l2, r2, lucky.get(j - 1), lucky.get(j) - 1);
			long rev = intersect(l2, r2, lucky.get(i) + 1, lucky.get(i + 1)) * intersect(l1, r1, lucky.get(j - 1), lucky.get(j) - 1); 
			if(k == 1 && rev > 0) rev--; 
			ans += rev;
			j++;
			i++;
		}
		out.println(1.0 * ans / (1l * (r1 - l1 + 1) * (r2 - l2 + 1)));
		out.flush();
		out.close();
	}
	
	static long intersect(long l1, long r1, long l2, long r2)
	{
		return Math.max(0, Math.min(r1, r2) - Math.max(l1, l2) + 1);
	}
	
	static long nxtLucky(Long n)
	{
		char[] a = (n + "").toCharArray();
		for(int i = a.length - 1; i >= 0; i--)
			if(a[i] == '4')
			{
				a[i] = '7';
				return Long.parseLong(new String(a));
			}
			else a[i] = '4';
		return Long.parseLong("4" + new String(a));
	}
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {br = new BufferedReader(new InputStreamReader(system));}
		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public String nextLine()throws IOException{return br.readLine();}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public double nextDouble() throws IOException {return Double.parseDouble(next());}
		public char nextChar()throws IOException{return next().charAt(0);}
		public Long nextLong()throws IOException{return Long.parseLong(next());}
		public boolean ready() throws IOException{return br.ready();}
		public void waitForInput(){for(long i = 0; i < 3e9; i++);}
	}
}