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.util.LinkedList;
import java.util.Scanner;

public class D {
    static LinkedList<Integer> numbs;

    public static void constuct(int rem, String cur) {
        if (rem == 0) {
            numbs.add(Integer.parseInt(cur));
            return;
        }
        constuct(rem - 1, cur + '4');
        constuct(rem - 1, cur + '7');
    }

    public static int getInter(int s1, int s2, int e1, int e2) {
        if(s1>e2||s2<e1) return 0;
        if(s1<=e2&&s1>=e1) {
            return Math.min(s2,e2)-s1+1;
        }else {
            return Math.min(s2,e2)-e1+1;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        numbs = new LinkedList<Integer>();
        for (int i = 1; i <= 9; i++)
            constuct(i, "");
        Integer[] numb = new Integer[numbs.size()];
        numbs.toArray(numb);
        double res = 0;
        int p1 = sc.nextInt(), p2 = sc.nextInt(), v1 = sc.nextInt(), v2 = sc
                .nextInt(), k = sc.nextInt();
        double pDen = p2 - p1 + 1;
        double vDen = v2 - v1 + 1;
        for (int i = 0; i + k-1 < numb.length; i++) {
            int stIdx = i;
            int endIdx = i + k-1;
            double add = 1, add1 = 1;
            if (endIdx + 1 == numb.length || numb[endIdx + 1] > p2) {
                add *= ((getInter(numb[endIdx], 1000000001, p1, p2)) / pDen);
            } else {
                add *= ((getInter(numb[endIdx], numb[endIdx + 1]-1, p1, p2)) / pDen);
            }
            if (endIdx + 1 == numb.length || numb[endIdx + 1] > v2) {
                add1 *= ((getInter(numb[endIdx], 1000000001, v1, v2)) / vDen);
            } else {
                add1 *= ((getInter(numb[endIdx], numb[endIdx + 1]-1, v1, v2)) / vDen);
            }
            if(stIdx == 0 || numb[stIdx - 1] < v1){
                add *= ((getInter(0, numb[stIdx], v1, v2)) / vDen);
            }
            else{add *= ((getInter( numb[stIdx - 1]+1,numb[stIdx], v1, v2)) / vDen);
            }
            if(stIdx == 0 || numb[stIdx - 1] < p1){
                add1 *= ((getInter(0,numb[stIdx],  p1, p2)) / pDen);
            }
            else{
            add1 *= ((getInter(numb[stIdx-1]+1, numb[stIdx ], p1, p2)) / pDen);
            }
            res += add;
            res += add1;
            if(stIdx==endIdx&&numb[stIdx]<=v2&&numb[stIdx]>=v1&&numb[stIdx]<=p2&&numb[stIdx]>=p1)
                res-=(1/vDen)*(1/pDen);
        }
        System.out.println(Math.min(res,1));
    }
}