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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

/**
 * @author Mubtasim Shahriar
 */

public class PinkSlips {

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
		int t = sc.nextInt();
//        int t = 1;
        while (t-- != 0) {
            solver.solve(sc, out);
        }
        out.close();

    }

    static class Solver {
        double ans;
        double eps = 1e-9;
        public void solve(InputReader sc, PrintWriter out) {
            ans = 0;
            double c = sc.nextDouble();
            double m = sc.nextDouble();
            double p = sc.nextDouble();
            double v = sc.nextDouble();
            rec(1.0,c,m,p,v);
            out.println(ans);
        }

        private void rec(double pp, double c, double m, double p, double v) {
            ans += pp;
            if(c>eps) {
                double take = Math.min(c,v);
                rec(pp*c,c-take, (m>eps ? m+take/2 : 0), p+take/2, v);
            }
            if(m>eps) {
                double take = Math.min(m,v);
                rec(pp*m, (c>eps ? c+take/2 : 0), m-take, p+take/2, v);
            }
        }

    }

    static void sort(int[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
    }

    static void sort(long[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
    }

    static void sortDec(int[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
        int l = 0;
        int r = n - 1;
        while (l < r) {
            arr[l] ^= arr[r];
            arr[r] ^= arr[l];
            arr[l] ^= arr[r];
            l++;
            r--;
        }
    }

    static void sortDec(long[] arr) {
        Random rand = new Random();
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int idx = rand.nextInt(n);
            if (idx == i) continue;
            arr[i] ^= arr[idx];
            arr[idx] ^= arr[i];
            arr[i] ^= arr[idx];
        }
        Arrays.sort(arr);
        int l = 0;
        int r = n - 1;
        while (l < r) {
            arr[l] ^= arr[r];
            arr[r] ^= arr[l];
            arr[l] ^= arr[r];
            l++;
            r--;
        }
    }

    static class InputReader {
        private boolean finished = false;

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int peek() {
            if (numChars == -1) {
                return -1;
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r') {
                    buf.appendCodePoint(c);
                }
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0) {
                s = readLine0();
            }
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines) {
                return readLine();
            } else {
                return readLine0();
            }
        }

        public BigInteger readBigInteger() {
            try {
                return new BigInteger(nextString());
            } catch (NumberFormatException e) {
                throw new InputMismatchException();
            }
        }

        public char nextCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public boolean isExhausted() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1) {
                read();
            }
            return value == -1;
        }

        public String next() {
            return nextString();
        }

        public SpaceCharFilter getFilter() {
            return filter;
        }

        public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) array[i] = nextInt();
            return array;
        }

        public int[] nextSortedIntArray(int n) {
            int array[] = nextIntArray(n);
            Arrays.sort(array);
            return array;
        }

        public int[] nextSumIntArray(int n) {
            int[] array = new int[n];
            array[0] = nextInt();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
            return array;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; ++i) array[i] = nextLong();
            return array;
        }

        public long[] nextSumLongArray(int n) {
            long[] array = new long[n];
            array[0] = nextInt();
            for (int i = 1; i < n; ++i) array[i] = array[i - 1] + nextInt();
            return array;
        }

        public long[] nextSortedLongArray(int n) {
            long array[] = nextLongArray(n);
            Arrays.sort(array);
            return array;
        }
    }


}