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 CF;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;

public class F {
	static int INF = (int)1e9;
	public static void main(String[] args) throws Exception
	{
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int pl = sc.nextInt(), pr = sc.nextInt(), vl = sc.nextInt(), vr = sc.nextInt(), k = sc.nextInt();
		int [] lucky = new int[1022];
		Queue<Integer> q = new LinkedList<Integer>();
		q.add(4);
		q.add(7);
		for (int i = 0; i < lucky.length; i++) {
			lucky[i] = q.remove();
			q.add(lucky[i]*10+4);
			q.add(lucky[i]*10+7);
		}
		long ans = 0;
		for (int i = 0, j = i+k-1; j < lucky.length; ++i, ++j) {
			int sl = i == 0?1:lucky[i-1]+1, sr = lucky[i]; 
			int tl = lucky[j], tr = j+1 >= lucky.length?INF:lucky[j+1]-1;
			ans += range(sl, sr, pl, pr)*range(tl, tr, vl, vr);
			long tmp = range(sl, sr, vl, vr)*range(tl, tr, pl, pr);
			if(k == 1 && tmp > 0) tmp--;
			ans += tmp;
		}
		out.println(1.0 * ans / (1l*(pr-pl+1)*(vr-vl+1)));
		out.flush();
		out.close();
	}
	static long range(long l, long r, long ll, long rr){
		return Math.max(0, Math.min(r, rr) - Math.max(l, ll) + 1);
	}
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s)
		{
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader fileReader)
		{
			br = new BufferedReader(fileReader);
		}

		public String next() throws IOException
		{
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException
		{
			return br.readLine();
		}

		public boolean ready() throws IOException
		{
			return br.ready();
		}
	}
}