Problem: After defeating a Blacklist Rival, you get a chance to draw 1 reward slip out of x hidden valid slips. Initially, x=3 and these hidden valid slips are Cash Slip, Impound Strike Release Marker and Pink Slip of Rival's Car. Initially, the probability of drawing these in a random guess are c, m, and p, respectively. There is also a volatility factor v. You can play any number of Rival Races as long as you don't draw a Pink Slip. Assume that you win each race and get a chance to draw a reward slip. In each draw, you draw one of the x valid items with their respective probabilities. Suppose you draw a particular item and its probability of drawing before the draw was a. Then,

  * If the item was a Pink Slip, the quest is over, and you will not play any more races. 
  * Otherwise, 
    1. If a≤ v, the probability of the item drawn becomes 0 and the item is no longer a valid item for all the further draws, reducing x by 1. Moreover, the reduced probability a is distributed equally among the other remaining valid items. 
    2. If a > v, the probability of the item drawn reduces by v and the reduced probability is distributed equally among the other valid items. 



For example,

  * If (c,m,p)=(0.2,0.1,0.7) and v=0.1, after drawing Cash, the new probabilities will be (0.1,0.15,0.75). 
  * If (c,m,p)=(0.1,0.2,0.7) and v=0.2, after drawing Cash, the new probabilities will be (Invalid,0.25,0.75). 
  * If (c,m,p)=(0.2,Invalid,0.8) and v=0.1, after drawing Cash, the new probabilities will be (0.1,Invalid,0.9). 
  * If (c,m,p)=(0.1,Invalid,0.9) and v=0.2, after drawing Cash, the new probabilities will be (Invalid,Invalid,1.0). 



You need the cars of Rivals. So, you need to find the expected number of races that you must play in order to draw a pink slip.

Input

The first line of input contains a single integer t (1≤ t≤ 10) — the number of test cases.

The first and the only line of each test case contains four real numbers c, m, p and v (0 < c,m,p < 1, c+m+p=1, 0.1≤ v≤ 0.9).

Additionally, it is guaranteed that each of c, m, p and v have at most 4 decimal places.

Output

For each test case, output a single line containing a single real number — the expected number of races that you must play in order to draw a Pink Slip.

Your answer is considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Example

Input


4
0.2 0.2 0.6 0.2
0.4 0.2 0.4 0.8
0.4998 0.4998 0.0004 0.1666
0.3125 0.6561 0.0314 0.2048


Output


1.532000000000
1.860000000000
5.005050776521
4.260163673896

Note

For the first test case, the possible drawing sequences are: 

  * P with a probability of 0.6; 
  * CP with a probability of 0.2⋅ 0.7 = 0.14; 
  * CMP with a probability of 0.2⋅ 0.3⋅ 0.9 = 0.054; 
  * CMMP with a probability of 0.2⋅ 0.3⋅ 0.1⋅ 1 = 0.006; 
  * MP with a probability of 0.2⋅ 0.7 = 0.14; 
  * MCP with a probability of 0.2⋅ 0.3⋅ 0.9 = 0.054; 
  * MCCP with a probability of 0.2⋅ 0.3⋅ 0.1⋅ 1 = 0.006. 

So, the expected number of races is equal to 1⋅ 0.6 + 2⋅ 0.14 + 3⋅ 0.054 + 4⋅ 0.006 + 2⋅ 0.14 + 3⋅ 0.054 + 4⋅ 0.006 = 1.532.

For the second test case, the possible drawing sequences are: 

  * P with a probability of 0.4; 
  * CP with a probability of 0.4⋅ 0.6 = 0.24; 
  * CMP with a probability of 0.4⋅ 0.4⋅ 1 = 0.16; 
  * MP with a probability of 0.2⋅ 0.5 = 0.1; 
  * MCP with a probability of 0.2⋅ 0.5⋅ 1 = 0.1. 



So, the expected number of races is equal to 1⋅ 0.4 + 2⋅ 0.24 + 3⋅ 0.16 + 2⋅ 0.1 + 3⋅ 0.1 = 1.86.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main{
    public static long mod = (long)1e9+7;
    public static ArrayList<Integer>[] graph;
    public static void main(String[] args) {
        InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
        int t = 1;
        t = in.nextInt();
        for(int i = 1;i<=t ;i++){
            solve(in,out);
        }
        out.close();
    }
    public static double expected = 0.00000000000000;
    private static void solve(InputReader in, PrintWriter out) {
        expected = 0.0000000000000;
        double c = in.nextDouble();
        double m = in.nextDouble();
        double p = in.nextDouble();
        double v = in.nextDouble();
        go(c,m,p,v,1.000000000000,1); 
        out.println(expected);
    }
    private static void go(double c, double m, double p, double v,double probab, int i) {
        if(not_equal(c,0.0)){
            if(less_than_equal(c, v)){
                if(not_equal(m, 0.0)){
                    go(0.0,m + (c/2.0),p+(c/2.0),v,probab*c,i+1);
                }
                else{
                    go(0.0,m,p+c,v,probab*c,i+1);
                }
                
            }
            else{
                if(not_equal(m, 0.0)){
                    go(c-v,m+ (v/2.0),(p+(v/2.0)),v,probab*c,i+1);
                }
                else{
                    go(c-v,m,p+v,v,probab*c,i+1);
                }
            }
        }
        if(not_equal(m,0.0)){
            if(less_than_equal(m,v)){
                if(not_equal(c,0.0)){
                    go(c + (m/2.0),0.0,p+(m/2.0),v,probab*m,i+1);
                }
                else{
                    go(c,0.0,p+m,v,probab*m,i+1);
                }
            }
            else{
                if(not_equal(c, 0.0)){
                    go(c + (v/2.0),m - v,p+(v/2.0),v,probab*m,i+1);
                }
                else{
                    go(c,m-v,p+v,v,probab*m,i+1);
                }
            }
                
        }
        //System.out.println(i+" "+probab+" "+p);
        expected += (i*(probab*p));
    }
    private static boolean not_equal(double c,double b) {
        //double zero = 0.000000;
        double eps = 0.0000001;
        if(Math.abs(c-b) >= eps) return true;
        else return false;
    }
    private static boolean less_than_equal(double a,double b){
        return !not_equal(a,b) || a<b;
    }
}
class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;
 
    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }
 
    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }
 
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble(){
        double d = Double.parseDouble(next());
        d += 0.000000000000;
        return d;
    }
    public int[] readIntArray(int size){
        int[] list = new int[size];
        for(int i = 0;i<size;i++) list[i] = nextInt();
        return list;
    }
    public long[] readLongArray(int size){
        long[] list = new long[size];
        for(int i = 0;i<size;i++) list[i] = nextLong();
        return list;
    }
    public double[] readDoubleArray(int size){
        double[] list = new double[size];
        for(int i = 0;i<size;i++) list[i] = nextDouble();
        return list;
    }
    public String linereader() {
        String s = null;
        try{
            s = reader.readLine();
        }
        catch (IOException e) {
            throw new RuntimeException(e);
        }
        return s;
    }
 
}
class Pair<T extends Comparable<T>,K extends Comparable<K> > implements Comparable<Pair<T,K>>{
    T first;
    K second;
    public Pair(T first, K second){
        this.first  = first;
        this.second = second;
    }
    @Override
    public String toString(){
        return first+" "+second;
    }
    @Override
    public int compareTo(Pair<T,K> o) {
        // TODO Auto-generated method stub
        if((first).compareTo(o.first)!=0) return first.compareTo(o.first);
        else return second.compareTo(o.second);
    }

}