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.*;


public class Main {

	int[] lucky;
	int count;
	
	void gen(int x,int deep){
		if(deep>8)return;
		int a=x*10+4;
		int b=x*10+7;
		lucky[count++]=a;
		lucky[count++]=b;
		gen(a,deep+1);
		gen(b,deep+1);
	}
	
	void solve() throws IOException {
		lucky=new int[1026];
		count=0;
		gen(0,0);
		lucky[count++]=0;
		lucky[count++]=1000000001;
		for(int i=1;i<count;i++)
			for(int j=0;j<count-i;j++)
				if(lucky[j]>lucky[j+1]){
					int tmp=lucky[j];
					lucky[j]=lucky[j+1];
					lucky[j+1]=tmp;
				}
		
		int xl=nextInt();
		int xr=nextInt();
		int yl=nextInt();
		int yr=nextInt();
		int k=nextInt();
		long c=0;
		for(int i=1;i<count-1;i++){
			if(lucky[i]<xl)continue;
			
			int j=i+k-1;
			if(j<count&&lucky[j]<=yr&&lucky[j+1]>yl){
				long a;
				int l;
				int r;
				if(lucky[i-1]<xl)
					l=xl;
				else
					l=lucky[i-1]+1;
				if(lucky[i]<xr)
					r=lucky[i];
				else
					r=xr;
				/*if(i==0)
					a=lucky[i]-xl+1;
				else
					if(lucky[i-1]<xl)
						a=lucky[i]-xl+1;
					else
						a=lucky[i]-lucky[i-1];*/a=r-l+1;
				long b;
				if(yl>lucky[j])
					l=yl;
				else
					l=lucky[j];
				if(yr<lucky[j+1])
					r=yr;
				else
					r=lucky[j+1]-1;
				b=r-l+1;
				/*if(j==count-1)
					b=yr-lucky[j]+1;
				else
					if(lucky[j+1]>yr)
						b=yr-lucky[j]+1;
					else
						b=lucky[j+1]-lucky[j];*/
				c+=a*b;
			}		
			if(lucky[i]>xr)break;
		}
		int tmp=xl;
		xl=yl;
		yl=tmp;
		tmp=xr;
		xr=yr;
		yr=tmp;
		for(int i=1;i<count-1;i++){
			if(lucky[i]<xl)continue;			
			int j=i+k-1;
			if(j<count&&lucky[j]<=yr&&lucky[j+1]>yl){
				long a;
				int l;
				int r;
				if(lucky[i-1]<xl)
					l=xl;
				else
					l=lucky[i-1]+1;
				if(lucky[i]<xr)
					r=lucky[i];
				else
					r=xr;
				/*if(i==0)
					a=lucky[i]-xl+1;
				else
					if(lucky[i-1]<xl)
						a=lucky[i]-xl+1;
					else
						a=lucky[i]-lucky[i-1];*/a=r-l+1;
				long b;
				if(yl>lucky[j])
					l=yl;
				else
					l=lucky[j];
				boolean f=false;			
				if(l==r)f=true;
				if(yr<lucky[j+1])
					r=yr;
				else
					r=lucky[j+1]-1;
				b=r-l+1;
				/*if(j==count-1)
					b=yr-lucky[j]+1;
				else
					if(lucky[j+1]>yr)
						b=yr-lucky[j]+1;
					else
						b=lucky[j+1]-lucky[j];*/
				/*if(!f)
					c+=a*b;
				else
					c+=(a-1)*b+(b-1)*a;*/
				c+=a*b;
				if(f)c--;
				
			}	
			if(lucky[i]>xr)break;
		}
		long d=(long)(xr-xl+1)*(long)(yr-yl+1);
		double res=(double)c/(double)d;
		out.printf(Locale.US,"%.12f",res);
	}

	public static void main(String[] args) throws IOException {
		new Main().run();
	}

	void run() throws IOException {
		reader = new BufferedReader(new InputStreamReader(System.in));
		tokenizer = null;
		out = new PrintWriter(new OutputStreamWriter(System.out));
		solve();
		reader.close();
		out.flush();

	}

	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter out;

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

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

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

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}
}