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 Main implements Runnable {
	final int UB = 1000000000;
        
	ArrayList<Integer> tmp_lucky = new ArrayList<Integer>();
        
	void gen(long cur) {
		if (cur > UB) return;
		tmp_lucky.add((int)cur); gen(10*cur+4); gen(10*cur+7);
	}
        
	double prob(int x, int y, int s, int e) {
		int tx = Math.max(x, s), ty = Math.min(y, e);           
		return (tx <= ty) ? (ty-tx+1.0)/(y-x+1) : 0.0;
	}
        
	public void run() {
		tmp_lucky.add(0); tmp_lucky.add(UB+1);
		gen(4); gen(7); Collections.sort(tmp_lucky);

		int lucky[] = new int[tmp_lucky.size()];
		for (int i = 0; i < lucky.length; ++i) lucky[i] = tmp_lucky.get(i);
                
		int pl = nextInt(), pr = nextInt(), vl = nextInt(), vr = nextInt(), k = nextInt();
        
		double answer = 0.0;
                
		for (int first = 1; first+k < lucky.length; ++first) {
			int a1 = lucky[first-1]+1, a2 = lucky[first];
			int b1 = lucky[first+k-1], b2 = lucky[first+k]-1;

			answer += prob(pl, pr, a1, a2) * prob(vl, vr, b1, b2);
			answer += prob(pl, pr, b1, b2) * prob(vl, vr, a1, a2);
			
			if (k == 1) answer -= prob(pl, pr, lucky[first], lucky[first]) * prob(vl, vr, lucky[first], lucky[first]);
		}
                
		output.printf("%.10f\n", answer);
		output.flush();
	}
        
    public static void main(String[] args) {
        //try { input = new BufferedReader(new InputStreamReader(new FileInputStream("input.txt"))); } catch (Exception e) {}
        new Main().run();
    }

    static BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter output = new PrintWriter(System.out);
    StringTokenizer tokenizer = null;

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

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

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

    String nextToken() {
        try
        {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(input.readLine());
            }

            return tokenizer.nextToken();
        } catch (Exception e) {
            return null;
        }
    }
}