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.BufferedInputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.Queue;

public class Main
{
	private ArrayList<Long> arr;
	private long vLeft;
	private long vRight;
	
	public void bfs(long x)
	{
		arr = new ArrayList<Long>();
		arr.add((long)4);
		arr.add((long)7);
		Queue<Long> q = new LinkedList<Long>();
		q.offer((long)4);
		q.offer((long)7);
		int[] dx = {4, 7};
		while(!q.isEmpty())
		{
			long y = q.poll();
			for(int i = 0;i < 2;++i)
			{
				long yNext = 10 * y + dx[i];
				arr.add(yNext);
				q.offer(yNext);
				if(yNext > x)
				{
					return;
				}
			}
		}
	}
	
	public long countLeft(int id, int k)
	{
		if(id >= k - 1)
		{
			return getIntersection(id == k - 1 ? (long)1 : arr.get(id -k) + 1, arr.get(id - k + 1), vLeft, vRight);
		}
		else
		{
			return 0;
		}
	}
	
	public long countRight(int id, int k)
	{
		if(id <= arr.size() - k)
		{
			return getIntersection(arr.get(id + k - 1), id == arr.size() - k ? (long)(1e10) : arr.get(id + k) - 1, vLeft, vRight);
		}
		else
		{
			return 0;
		}
	}
	
	public long getIntersection(long a, long b, long c, long d)
	{
		if(d < a || c > b)
		{
			return 0;
		}
		else
		{
			return Math.min(b, d) - Math.max(a, c) + 1;
		}
	}
	
	public void foo()
	{
		MyScanner scan = new MyScanner();
		long pLeft = scan.nextInt();
		long pRight = scan.nextInt();
		vLeft = scan.nextInt();
		vRight = scan.nextInt();
		int k = scan.nextInt();
		bfs(Math.max(pRight, vRight));
		long total = (pRight - pLeft + 1) * (vRight - vLeft + 1);
		long sum = 0;
		int id = 0;
		for(id = 0;arr.get(id) < pLeft;++id);
		while(pLeft <= pRight)
		{
			long t = arr.get(id);
			if(pLeft == t)
			{
				if(1 == k && getIntersection(pLeft, pLeft, vLeft, vRight) > 0)
				{
					sum += countLeft(id, k) + countRight(id, k) - 1;
				}
				else
				{
					sum += countLeft(id, k) + countRight(id, k);
				}
				++pLeft;
				++id;
			}
			else
			{
				if(pRight < t)
				{
					sum += (long)(pRight - pLeft + 1) * (countLeft(id - 1, k) + countRight(id, k));
					break;
				}
				else
				{
					sum += (long)(t - pLeft) * (countLeft(id - 1, k) + countRight(id, k));
					pLeft = t;
				}
			}
		}
		System.out.println((double)sum / total);
	}
	
	public static void main(String[] args)
	{
		new Main().foo();
	}
	
	class MyScanner
	{
	    private byte[] buf = new byte[1024];
	    private int curChar;
	    private int numChars;
	    BufferedInputStream bis = new BufferedInputStream(System.in);

	    public int read() 
	    {
	        if (-1 == numChars)
	        {
	        	throw new InputMismatchException();
	        }
	        if (curChar >= numChars)
	        {
	            curChar = 0;
	            try 
	            {
	                numChars = bis.read(buf);
	            }
	            catch (IOException e)
	            {
	                throw new InputMismatchException();
	            }
	            if (numChars <= 0)
	            {
	            	return -1;
	            }
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() 
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        int sgn = 1;
	        if (c == '-') 
	        {
	            sgn = -1;
	            c = read();
	        }
	        int res = 0;
	        do 
	        {
	            if (c < '0' || c > '9')
	            {
	            	throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }
	    
	    public String next()
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        StringBuilder res = new StringBuilder();
	        do 
	        {
	            res.appendCodePoint(c);
	            c = read();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    private boolean isSpaceChar(int c) 
	    {
	        return ' ' == c || '\n' == c || '\r' == c || '\t' == c || -1 == c;
	    }
	}
}