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.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class D84 {

	static boolean test = false;

	private void solve() throws Throwable, IOException {

		int al = iread(), ar = iread(), bl = iread(), br = iread(), k = iread();

		List<Integer> all = new ArrayList<Integer>();
		buildAll(0, Math.max(ar, br), all);
		all.add(Math.max(ar, br) + 2);
		
		Collections.sort(all);
		
		long res = 0;
		
		for (int i = 1; i < all.size(); i++) {
			for (int bi = 0; bi < 2; bi++) {
				int mini, maxi;
				if(bi == 0){
					mini = all.get(i-1) + 1;
					maxi = all.get(i) - 1;
				} else {
					mini = all.get(i);
					maxi = mini;
				}
				
				mini = Math.max(mini, al);
				maxi = Math.min(maxi, ar);
				
				if(mini > maxi){
					continue;
				}
				for (int j = 1; j < all.size(); j++) {
					for (int bj = 0; bj < 2; bj++) {
						int cnt = Math.max(i, j) - Math.min(i, j);
						if((i >= j && bi ==1) || (j >= i && bj == 1)){
							cnt ++;
						}
						if(cnt != k){
							continue;
						}
						
						int minj, maxj;
						if(bj == 0){
							minj = all.get(j - 1) + 1;
							maxj = all.get(j)  - 1;
						} else {
							minj = all.get(j);
							maxj = minj;
						}
						minj = Math.max(minj, bl);
						maxj = Math.min(maxj, br);
						if(minj > maxj){
							continue;
						}
						res += (maxi - mini + 1 ) * (long)(maxj - minj + 1);
					}
				}
			}
		}
		System.out.printf("%.15f", res / (double)((ar - al + 1) * (long)(br - bl + 1)));
	}

	private void buildAll(long i, long max, List<Integer> all) {
		
		if(i > max){
			return;
		} else {
			all.add((int) i);
		}
		buildAll(i*10 + 4, max, all);
		buildAll(i*10 + 7, max, all);
	}

	public int iread() throws Exception {
		return Integer.parseInt(wread());
	}

	public double dread() throws Exception {
		return Double.parseDouble(wread());
	}

	public long lread() throws Exception {
		return Long.parseLong(wread());
	}

	public String wread() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) throws Throwable {
		new D84().solve();
		out.close();
	}

	public D84() throws Throwable {
		if (test) {
			in = new BufferedReader(new FileReader(new File(testDataFile)));
		} else {
			new BufferedReader(inp);
		}
	}

	static InputStreamReader inp = new InputStreamReader(System.in);
	static BufferedReader in = new BufferedReader(inp);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

	static String testDataFile = "testdata.txt";
	BufferedReader reader = null;
}