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.*;
import java.util.*;
import java.math.*;

public class D implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	private void solve() throws IOException {
		long fiLb = nextLong(), fiRb = nextLong();
		long seLb = nextLong(), seRb = nextLong();
		int k = nextInt();

		long all = (fiRb - fiLb + 1) * (seRb - seLb + 1);
		long good = 0;

		long[] goodNumbers = generateGoodNumbers();

		good += getCount(fiLb, fiRb, seLb, seRb, k, goodNumbers);
		good += getCount(seLb, seRb, fiLb, fiRb, k, goodNumbers);

		if (k == 1) {
			for (long goodNumber : goodNumbers) {
				if (fiLb <= goodNumber && goodNumber <= fiRb
						&& seLb <= goodNumber && goodNumber <= seRb) {
					--good;
				}
			}
		}

		double result = (double) good / all;

		out.println(result);
	}

	private long getCount(long fiLb, long fiRb, long seLb, long seRb, int k,
			long[] goodNumbers) {
		long good = 0;

		for (int i = 0; i < goodNumbers.length; i++) {
			long iLb = (i == 0) ? 1 : goodNumbers[i - 1] + 1;
			long iRb = goodNumbers[i];

			for (int j = -1; j < goodNumbers.length; j++) {
				long jLb = (j == -1) ? 1 : goodNumbers[j];
				long jRb = (j + 1 == goodNumbers.length) ? Integer.MAX_VALUE
						: goodNumbers[j + 1] - 1;

				int count = j - i + 1;

				if (count == k) {
					good += intersect(fiLb, fiRb, iLb, iRb)
							* intersect(seLb, seRb, jLb, jRb);
				}
			}
		}

		return good;
	}

	private long intersect(long x0, long y0, long x1, long y1) {
		long x = Math.max(x0, x1);
		long y = Math.min(y0, y1);
		return Math.max(0, y - x + 1);
	}

	private long[] generateGoodNumbers() {
		final long maxValue = 4444444444L;
		final long[] goodDigits = { 4, 7 };
		List<Long> result = new ArrayList<>();
		for (long digit : goodDigits) {
			rec(digit, maxValue, goodDigits, result);
		}
		Collections.sort(result);
		long[] resultArr = new long[result.size()];
		for (int i = 0; i < result.size(); i++) {
			resultArr[i] = result.get(i);
		}
		return resultArr;
	}

	private void rec(long n, long maxValue, long[] goodDigits, List<Long> result) {
		if (n <= maxValue) {
			result.add(n);
			for (long digit : goodDigits) {
				rec(10 * n + digit, maxValue, goodDigits, result);
			}
		}
	}

	public static void main(String[] args) {
		// final boolean oldChecker = false;
		//
		// if (oldChecker)
		// new Thread(null, new Template(), "yarrr", 1 << 24).start();
		// else
		new D().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

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