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.Arrays;
import java.util.LinkedList;
public class prob109B {

    static LinkedList<Integer> lucky = new LinkedList<Integer>();
    static long max;
    public static void generate(String cur){
        long x = Long.parseLong(cur);
        if(x > max)return;
        lucky.add(Integer.parseInt(cur));
        generate(cur + "4");
        generate(cur + "7");
    }
    public static void main(String[] args)throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String [] use = br.readLine().split(" ");
        long pl = Long.parseLong(use[0]);
        long pu = Long.parseLong(use[1]);
        long vl = Long.parseLong(use[2]);
        long vu = Long.parseLong(use[3]);
        int k = Integer.parseInt(use[4]);
        long [] tmp = new long [] {pl, pu, vl, vu};
        Arrays.sort(tmp);
        max = tmp[3];
        generate("4");
        generate("7");
        int [] luckyNums = new int [lucky.size()];
        for(int i = 0 ; i < luckyNums.length ; ++i)luckyNums[i] = lucky.get(i);
        Arrays.sort(luckyNums);
        double s = 0;
        for(int i = 0 ; i < luckyNums.length - k + 1; ++i){
            int start = i;
            int bstart = i - 1;
            int end = i + k - 1;
            int aend = end + 1;
            long t1 = Math.max(bstart < 0 ? 0 : luckyNums[bstart] + 1, pl);
            long t2 = Math.min(luckyNums[start], pu);
            long t3 = Math.max(luckyNums[end], vl);
            long t4 = Math.min(aend >= luckyNums.length ? (int)1e9 : luckyNums[aend] - 1, vu);
            long comp1 = 0, comp2 = 0;
            if(t1 <= t2)comp1 = t2 - t1 + 1;
            if(t3 <= t4)comp2 = t4 - t3 + 1;
            s += comp1 * comp2;
            t1 = Math.max(bstart < 0 ? 0 : luckyNums[bstart] + 1, vl);
            t2 = Math.min(luckyNums[start], vu);
            t3 = Math.max(luckyNums[end], pl);
            t4 = Math.min(aend >= luckyNums.length ? (int)1e9 : luckyNums[aend] - 1, pu);
            comp1 = 0;
            comp2 = 0;
            if(t1 <= t2)comp1 = t2 - t1 + 1;
            if(t3 <= t4)comp2 = t4 - t3 + 1;
            s += comp1 * comp2;
            t1 = Math.max(luckyNums[start], pl);
            t2 = Math.min(luckyNums[start], pu);
            t3 = Math.max(luckyNums[start], vl);
            t4 = Math.min(luckyNums[start], vu);
            comp1 = 0;comp2 = 0;
            if(t1 <= t2)comp1 = t2 - t1 + 1;
            if(t3 <= t4)comp2 = t4 - t3 + 1;
            if(k == 1 && comp1 != 0 && comp2 != 0)s--;
        }
        double tot = (pu - pl + 1) * (vu - vl + 1);
        System.out.println(s / tot);
    }
}