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.math.BigDecimal;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class P110D {

    public static void main(String[] args) {

        Scanner inScanner = new Scanner(System.in);
        int pl = inScanner.nextInt();
        int pr = inScanner.nextInt();
        int vl = inScanner.nextInt();
        int vr = inScanner.nextInt();
        int k = inScanner.nextInt();

        long denominateur = (long) (pr - pl + 1) * (long) (vr - vl + 1);

        List<Integer> luckyNumbers = generateLuckyNumbers(Math.min(pl, vl),
                Math.max(pr, vr));

        if (luckyNumbers.size() < k) {
            System.out.println(0);
            return;
        }

        luckyNumbers.add(0, Math.min(pl, vl) - 1);
        luckyNumbers.add(Math.max(pr, vr) + 1);

        double result = 0;

        for (int i = 1; i < luckyNumbers.size() - k; i++) {

            int minLeft = luckyNumbers.get(i - 1) + 1;
            int minRight = luckyNumbers.get(i);

            int maxLeft = luckyNumbers.get(i + k - 1);
            int maxRight = luckyNumbers.get(i + k) - 1;

            long possibilitiesPAtLeft = Math.max(0, Math.min(minRight, pr)
                    - Math.max(minLeft, pl) + 1);
            long possibilitiesVAtRight = Math.max(0, Math.min(maxRight, vr)
                    - Math.max(maxLeft, vl) + 1);

            long possibilitiesVAtLeft = Math.max(0, Math.min(minRight, vr)
                    - Math.max(minLeft, vl) + 1);
            long possibilitiesPAtRight = Math.max(0, Math.min(maxRight, pr)
                    - Math.max(maxLeft, pl) + 1);

            long possibilities = possibilitiesPAtLeft * possibilitiesVAtRight
                    + possibilitiesVAtLeft * possibilitiesPAtRight;

            if (k == 1 && Math.min(minRight, pr) >= luckyNumbers.get(i)
                    && Math.min(minRight, vr) >= luckyNumbers.get(i)
                    && Math.max(maxLeft, pl) <= luckyNumbers.get(i)
                    && Math.max(maxLeft, vl) <= luckyNumbers.get(i))
                possibilities--;
            result += (double) possibilities / denominateur;
        }
        System.out.println(new BigDecimal(Double.toString(result))
                .toPlainString());
    }

    static List<Integer> generateLuckyNumbers(int l, int r) {
        List<Integer> allOfThem = generateUnorderedLuckyNumbers(9);
        List<Integer> returned = new ArrayList<Integer>();
        for (int lucky : allOfThem) {
            if (lucky >= l && lucky <= r && !returned.contains(lucky))
                returned.add(lucky);
        }
        Collections.sort(returned);
        return returned;
    }

    static List<Integer> generateUnorderedLuckyNumbers(int digits) {
        List<Integer> returnedList;
        if (digits == 1) {
            returnedList = new ArrayList<Integer>();
            returnedList.add(4);
            returnedList.add(7);
            return returnedList;
        }
        List<Integer> originList = generateUnorderedLuckyNumbers(digits - 1);
        returnedList = new ArrayList<Integer>(originList);
        for (int original : originList) {
            returnedList
                    .add(Integer.parseInt("4" + Integer.toString(original)));
            returnedList
                    .add(Integer.parseInt("7" + Integer.toString(original)));
        }
        return returnedList;
    }
}