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.IOException;
import java.io.InputStreamReader;

public class Contest84_2 {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        String[] s = in.readLine().split(" ");
        int pl = Integer.parseInt(s[0]);
        int pr = Integer.parseInt(s[1]);
        int vl = Integer.parseInt(s[2]);
        int vr = Integer.parseInt(s[3]);
        int k = Integer.parseInt(s[4]);
        int[] lucky = new int[2000];
        lucky[0] = 4;
        lucky[1] = 7;
        int m = 2;
        String[] zeros = { "0", "00", "000", "0000", "00000", "000000",
                "0000000", "00000000" };
        boolean flag = false;
        for (int i = 2; i <= 9; i++) {
            for (int j = 0; j < (1 << i); j++) {
                String curr = Integer.toBinaryString(j);
                if (curr.length() < i)
                    curr = zeros[i - curr.length() - 1] + curr;
                curr = curr.replace('0', '4');
                curr = curr.replace('1', '7');
                int a = Integer.parseInt(curr);
                // System.out.println(a);
                if (a > 1000000000) {
                    flag = true;
                    break;
                }
                lucky[m++] = a;
            }
            if (flag)
                break;
        }
        long res = 0;
        for (int i = 0; i < m; i++) {
            int limit1l = pl;
            int limit2l = vl;
            int limit1r = vr;
            int limit2r = pr;
            if (i != 0) {
                limit1l = Math.max(limit1l, lucky[i - 1] + 1);
                limit2l = Math.max(limit2l, lucky[i - 1] + 1);
            }
            if (i + k < m) {
                limit1r = Math.min(limit1r, lucky[i + k] - 1);
                limit2r = Math.min(limit2r, lucky[i + k] - 1);
            }
            int st = lucky[i];
            int end = lucky[i + k - 1];
            if (st == 0 || end == 0)
                break;
            long num1l = Math.min(st - limit1l + 1, pr - limit1l + 1);
            long num1r = Math.min(limit1r - end + 1, limit1r - vl + 1);
            if (num1l > 0 && num1r > 0) {
                // System.out.println(st+" "+end+" HOHO" + " " +
                // num1l+" "+num1r);
                res += num1l * num1r;
            }
            long num2l = Math.min(st - limit2l + 1, vr - limit2l + 1);
            long num2r = Math.min(limit2r - end + 1, limit2r - pl + 1);
            if (num2l > 0 && num2r > 0) {
                // System.out.println("HOHOHO" + " " + num2l+" "+num2r);
                res += num2l * num2r;
            }
        }
        // System.out.println(res);
        int intersect = 0;
        if(vl>=pl && vl<=pr && k==1) {
            for (int i = 0; i < m; i++) {
                if(lucky[i]>=vl && lucky[i]<=pr)
                    intersect++;
            }
        } else if(pl>=vl && pl<=vr && k==1) {
            for (int i = 0; i < m; i++) {
                if(lucky[i]>=pl && lucky[i]<=vr)
                    intersect++;
            }
        }
        //System.out.println(res + " "+intersect);
        double ress = res - intersect;
        long a = (pr - pl + 1);
        long b = (vr - vl + 1);
        double div = a * b;
        System.out.println(ress / div);
    }
}