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.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;
import static java.lang.Math.*;
import java.io.PrintWriter;
public class D84 {
	static Scanner in = new Scanner(System.in);
	static PrintWriter w = new PrintWriter(System.out, true);

	static int ni() {
		return in.nextInt();
	}

	static String nl() {
		return in.nextLine();
	}

	public static void main(String[] args) {
		int p1 = ni(), p2 = ni(), v1 = ni(), v2 = ni(), k = ni();
		int min  = min(p1, v1);
		int max = max(p2, v2);
		ArrayList<Integer> h = new ArrayList<Integer>();
		for (int i = 1; i <10; i++) {
			for (int j = 0; j < (1<<i); j++) {
				int d = 0;
				for (int l = 0; l < i; l++) 
					d = d*10 + (((j & (1<<l)) != 0) ? 7 : 4);
				h.add(d);
			}
		}
		Collections.sort(h);
		int[][] bounds = new int[2000][4];
		int ib = 0, p = 0;
		while (ib + k <= h.size()) {
			int[] a = bounds[ib];
			a[0] = p;
			a[1] = h.get(ib);
			a[2] = h.get(ib + k - 1);
			a[3] = (ib + k == h.size()) ? 1000000000 : (h.get(ib + k) - 1);
			ib++;
			p = a[1] + 1;
		}
		//w.println(Arrays.toString(bounds));
		long tc = 0, tco;
		for (int i =0; i < ib; i++) {
			int[] a = bounds[i];
			tco = tc;
			tc += pp(a[0], a[1], v1, v2)*pp(a[2], a[3], p1, p2);
			tc += pp(a[0], a[1], p1, p2)*pp(a[2], a[3], v1, v2);
			if (tc < 0) {
				tc = 0;
			}
			if (tco != tc && a[1]==a[2] && a[1] <= v2 && a[1] >= v1 && a[1] >= p1 && a[1] <= p2) tc--;
		}
		w.println(String.format("%1.12f", (tc * 1.0) / (((long)(v2 - v1 + 1)) * (p2 - p1 + 1))).replaceAll(",", "."));
	}
	
	static long pp(int i1, int i2, int i3, int i4) {
		if (i1 > i4 || i3 > i2) return 0;
		int r = min(i2, i4) - max(i1, i3) + 1;
		if (r < 0) {
			r = 0;
		}
		return r;
	}
}