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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {
	static ArrayList<Long> lucky;

	public static void bfs() {
		Queue<Long> q = new LinkedList<Long>();
		q.add(4l);
		q.add(7l);
		while (!q.isEmpty()) {
			long x = q.poll();
			lucky.add(x);
			if (x > (int) 1e9) {
				break;
			}
			q.add(Long.parseLong(x + "" + 4));
			q.add(Long.parseLong(x + "" + 7));
		}
	}

	public static long ways(int l1, int r1, long x1, long x2, int l2, int r2, Long y1, long y2) {
		long up1 = Math.min(r1, x2), low1 = Math.max(l1, x1), up2 = Math.min(r2, y2), low2 = Math.max(l2, y1);
		long ret = 1l * Math.max(up1 - low1 + 1, 0) * Math.max(up2 - low2 + 1, 0);
		up1 = Math.min(r2, x2);
		low1 = Math.max(l2, x1);
		up2 = Math.min(r1, y2);
		low2 = Math.max(l1, y1);
		ret += 1l * Math.max(up1 - low1 + 1, 0) * Math.max(up2 - low2 + 1, 0);
		if (x2 == y1 && y1 <= r2 && y1 >= l2 && y1 <= r1 && y1 >= l1) {
			ret--;
		}
		return ret;
	}

	public static void main(String[] args) throws IOException {
		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();
		lucky = new ArrayList<>();
		lucky.add(0l);
		bfs();
		long total = 0;

		for (int i = 1; i + k < lucky.size(); i++) {
			total += ways(pl, pr, lucky.get(i - 1) + 1, lucky.get(i), vl, vr, lucky.get(i + k - 1),
					lucky.get(i + k) - 1);
		}
		System.out.println(total / (1.0 * (vr - vl + 1) * (pr - pl + 1)));

		out.close();
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String f) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(f));
		}

		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 double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

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

		public int[] nextIntArray(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public int[] nextIntArray1(int n) throws IOException {
			int[] a = new int[n + 1];
			for (int i = 1; i <= n; i++)
				a[i] = nextInt();
			return a;
		}

		public int[] shuffle(int[] a, int n) {
			int[] b = new int[n];
			for (int i = 0; i < n; i++)
				b[i] = a[i];
			Random r = new Random();
			for (int i = 0; i < n; i++) {
				int j = i + r.nextInt(n - i);
				int t = b[i];
				b[i] = b[j];
				b[j] = t;
			}
			return b;
		}

		public int[] nextIntArraySorted(int n) throws IOException {
			int[] a = nextIntArray(n);
			a = shuffle(a, n);
			Arrays.sort(a);
			return a;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public long[] nextLongArray1(int n) throws IOException {
			long[] a = new long[n + 1];
			for (int i = 1; i <= n; i++)
				a[i] = nextLong();
			return a;
		}

		public long[] nextLongArraySorted(int n) throws IOException {
			long[] a = nextLongArray(n);
			Random r = new Random();
			for (int i = 0; i < n; i++) {
				int j = i + r.nextInt(n - i);
				long t = a[i];
				a[i] = a[j];
				a[j] = t;
			}
			Arrays.sort(a);
			return a;
		}
	}

}