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.math.*;
import java.util.*;
import static java.lang.Math.*;

public class BetaRound84_Div1_B implements Runnable {
	
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok;
	
	@Override
	public void run() {
		try {
			long t1 = System.currentTimeMillis();
			if (System.getProperty("ONLINE_JUDGE") == null) {
				in = new BufferedReader(new FileReader("input.txt"));
				out = new PrintWriter("output.txt");
			} else {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}
			tok = new StringTokenizer("");
			solve();
			in.close();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = " + (t2-t1));
			long m1 = Runtime.getRuntime().freeMemory();
			long m2 = Runtime.getRuntime().totalMemory();
			System.err.println("Memory = " + ((m2-m1)>>10));
		} catch (Throwable e) {
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	public static void main(String[] args) {
		new Thread(null, new BetaRound84_Div1_B(), "", 256 * (1L<<20)).start();
	}
	
	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}
	
	long readLong() throws IOException {
		return Long.parseLong(readString());
	}
	
	double readDouble() throws IOException {
		return Double.parseDouble(readString());
	}
	
	// solution
	
	long[] luckyNumbers() {
		ArrayList<Long> a = new ArrayList<Long>();
		for (int len = 1; len <= 9; len++) {
			for (int m = 0; m < (1 << len); m++) {
				long x = 0;
				for (int i = 0; i < len; i++) {
					if (((1 << i) & m) == 0) {
						x = 10 * x + 4;
					} else {
						x = 10 * x + 7;
					}
				}
				a.add(x);
			}
		}
		long[] b = new long[a.size()];
		for (int i = 0; i < a.size(); i++) {
			b[i] = a.get(i);
		}
		Arrays.sort(b);
		return b;
	}
	
	final long[] arr = luckyNumbers();
	
	long prev(long x) {
		if (x == -1) return -111;
		int i = Arrays.binarySearch(arr, x);
		if (i >= 0) {
			return arr[i];
		} else {
			i = -i-1;
			if (i == 0) return -111;
			return arr[i - 1];
		}
	}
	
	long next(long x) {
		if (x == -1) return -111;
		int i = Arrays.binarySearch(arr, x);
		if (i >= 0) {
			return arr[i];
		} else {
			i = -i-1;
			if (i == arr.length) return -111;
			return arr[i];
		}
	}
	
	long len(long a, long b) {
		if (b < a) return 0;
		return b - a + 1;
	}
	
	long count(long L, long R) {
		int i = Arrays.binarySearch(arr, L);
		int j = Arrays.binarySearch(arr, R);
		return max(0, j - i + 1);
	}
	
	long K;
	
	long sum(long a1, long a2, long b1, long b2) {

		long ans = 0;
		for (long L = a1; L <= a2 && L >= -11; L = next(L) + 1) {
			for (long R = b2; R >= b1 && R >= -11; R = prev(R) - 1) {
				long LL = next(L);
				long RR = prev(R);
				
				long LC = len(L, min(a2, LL));
				long RC = len(max(b1, RR), R);
				long c = count(LL, RR);
				if (c == K) {
					ans += LC * RC;
				}
			}
		}
		return ans;
	}
	
	void solve() throws IOException {
		long pl = readLong();
		long pr = readLong();
		long vl = readLong();
		long vr = readLong();
		K = readLong();
		
		long all = len(vl, vr) * len(pl, pr);
		long good = sum(vl, vr, pl, pr) + sum(pl, pr, vl, vr);
		
		if (K == 1) {
			HashSet<Long> set = new HashSet<Long>();
			for (long L = max(next(vl), next(pl)); L <= min(prev(vr), prev(pr)) && L >= -11; L = next(L) + 1) {
				set.add(L);
			}
			good -= set.size();
		}
		
		double ans = ((double) good) / all;
		
		out.printf(Locale.US, "%.12f", ans);
	}

}