Problem: There is a road with length l meters. The start of the road has coordinate 0, the end of the road has coordinate l.

There are two cars, the first standing at the start of the road and the second standing at the end of the road. They will start driving simultaneously. The first car will drive from the start to the end and the second car will drive from the end to the start.

Initially, they will drive with a speed of 1 meter per second. There are n flags at different coordinates a_1, a_2, …, a_n. Each time when any of two cars drives through a flag, the speed of that car increases by 1 meter per second.

Find how long will it take for cars to meet (to reach the same coordinate). 

Input

The first line contains one integer t (1 ≤ t ≤ 10^4): the number of test cases.

The first line of each test case contains two integers n, l (1 ≤ n ≤ 10^5, 1 ≤ l ≤ 10^9): the number of flags and the length of the road.

The second line contains n integers a_1, a_2, …, a_n in the increasing order (1 ≤ a_1 < a_2 < … < a_n < l).

It is guaranteed that the sum of n among all test cases does not exceed 10^5.

Output

For each test case print a single real number: the time required for cars to meet.

Your answer will be considered correct, if its absolute or relative error does not exceed 10^{-6}. More formally, if your answer is a and jury's answer is b, your answer will be considered correct if \frac{|a-b|}{max{(1, b)}} ≤ 10^{-6}.

Example

Input


5
2 10
1 9
1 10
1
5 7
1 2 3 4 6
2 1000000000
413470354 982876160
9 478
1 10 25 33 239 445 453 468 477


Output


3.000000000000000
3.666666666666667
2.047619047619048
329737645.750000000000000
53.700000000000000

Note

In the first test case cars will meet in the coordinate 5.

The first car will be in the coordinate 1 in 1 second and after that its speed will increase by 1 and will be equal to 2 meters per second. After 2 more seconds it will be in the coordinate 5. So, it will be in the coordinate 5 in 3 seconds.

The second car will be in the coordinate 9 in 1 second and after that its speed will increase by 1 and will be equal to 2 meters per second. After 2 more seconds it will be in the coordinate 5. So, it will be in the coordinate 5 in 3 seconds.

In the second test case after 1 second the first car will be in the coordinate 1 and will have the speed equal to 2 meters per second, the second car will be in the coordinate 9 and will have the speed equal to 1 meter per second. So, they will meet after (9-1)/(2+1) = 8/3 seconds. So, the answer is equal to 1 + 8/3 = 11/3.

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.Comparator;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Set;

public class Grakn_P3_V1 {

    public static void main (String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out	=	new OutputWriter(System.out);
        int t = in.readInt();
        for (int z=1;z<=t;z++){
            int n = in.readInt(), l = in.readInt();
            int[] a = IOUtils.readIntArray(in, n);
            double x = 0D;
            double y = l;

            double sx = 1D;
            double sy = 1D;

            double ans = 0D;
            int i = 0, j = n-1;

            while (i <= j) {
                double tx = (a[i] - x) / sx;
                double ty = (y - a[j]) / sy;

                if (Double.compare(tx, ty) == 0) {
                    x = x + (tx*sx);
                    y = y - (ty*sy);
                    ans = ans + ty;
                    i++;
                    j--;
                    sx = sx + 1;
                    sy = sy + 1;
                }
                else if (Double.compare(tx, ty) < 0) {
                    x = x + (tx*sx);
                    y = y - (tx*sy);
                    ans = ans + tx;
                    i++;
                    sx = sx + 1;
                }
                else {
                    x = x + (ty*sx);
                    y = y - (ty*sy);
                    ans = ans + ty;
                    j--;
                    sy = sy + 1;
                }
            }

            if (Double.compare(x,y) < 0) {
                double dist = y - x;
                double relativeSpeed = sx+sy;
                ans = ans + (dist / relativeSpeed);
            }
            out.printLine(BigDecimal.valueOf(ans).setScale(10, RoundingMode.CEILING).toPlainString());
        }
        out.close();
    }

    static class Fraction implements Comparable<Fraction>{
        long num, denom;

        public Fraction(long num, long denom) {
            this.num = num;
            this.denom = denom;
        }

        public boolean isNegative() {
            if((num > 0 && denom < 0) || (num < 0 && denom > 0)) {
                return true;
            }
            return false;
        }

        public boolean isValid() {
            return denom != 0;
        }

        public BigDecimal value() {
            return new BigDecimal(num).divide(new BigDecimal(denom), 10, RoundingMode.HALF_UP);
        }

        @Override
        public int compareTo(Fraction o) {
            long val = (this.num*o.denom - this.denom*o.num);
            if(val == 0) {
                return 0;
            }
            else if(val > 0) {
                return 1;
            }
            else {
                return -1;
            }
        }
    }

    static class FractionSortByAscending implements Comparator<Fraction> {

        @Override
        public int compare(Fraction o1, Fraction o2) {
            return o1.compareTo(o2);
        }
    }

    static class FractionUtils {

        // a >= b
        static long gcd(long a, long b)
        {
            if (b == 0)
                return a;
            return gcd(b, a % b);
        }


        static Fraction add(Fraction a, Fraction b) {
            long num = a.num*b.denom + b.num*a.denom;
            long denom = a.denom*b.denom;
            long gcd =  gcd(Math.max(num, denom), Math.min(num, denom));
            num /= gcd;
            denom /= gcd;
            return new Fraction(num, denom);
        }

        static Fraction sub(Fraction a, Fraction b) {
            long num = a.num*b.denom - b.num*a.denom;
            long denom = a.denom*b.denom;
            long gcd =  gcd(Math.max(num, denom), Math.min(num, denom));
            num /= gcd;
            denom /= gcd;
            return new Fraction(num, denom);
        }

        static Fraction multiply(Fraction a, Fraction b) {
            long num = a.num*b.num;
            long denom = a.denom*b.denom;
            long gcd =  gcd(Math.max(num, denom), Math.min(num, denom));
            num /= gcd;
            denom /= gcd;
            return new Fraction(num, denom);
        }
        static Fraction div(Fraction a, Fraction b) {
            if(a.denom == 0 || b.num == 0) {
                return null;
            }
            long num = a.num*b.denom;
            long denom = a.denom*b.num;
            long gcd =  gcd(Math.max(num, denom), Math.min(num, denom));
            num /= gcd;
            denom /= gcd;
            return new Fraction(num, denom);
        }

        static Fraction fractionWithDenomAsOne(long num) {
            return new Fraction(num, 1);
        }

    }

    /*static class Fraction implements Comparable<Fraction>{
        BigInteger num, denom;

        public Fraction(BigInteger num, BigInteger denom) {
            this.num = num;
            this.denom = denom;
        }

        public boolean isNegative() {
            if((num.compareTo(BigInteger.ZERO) > 0 && denom.compareTo(BigInteger.ZERO) < 0) || (num.compareTo(BigInteger.ZERO) < 0 && denom.compareTo(BigInteger.ZERO) > 0)) {
                return true;
            }
            return false;
        }

        public boolean isValid() {
            return denom.compareTo(BigInteger.ZERO) != 0;
        }

        public BigDecimal value() {
            return new BigDecimal(num).divide(new BigDecimal(denom), 10, RoundingMode.HALF_UP);
        }

        @Override
        public int compareTo(Fraction o) {
            BigInteger val1 = this.num.multiply(o.denom);
            BigInteger val2 = this.denom.multiply(o.num);
            BigInteger val = val1.subtract(val2);
            if(val.compareTo(BigInteger.ZERO) == 0) {
                return 0;
            }
            else if(val.compareTo(BigInteger.ZERO) > 0) {
                return 1;
            }
            else {
                return -1;
            }
        }
    }

    static class FractionSortByAscending implements Comparator<Fraction> {

        @Override
        public int compare(Fraction o1, Fraction o2) {
            return o1.compareTo(o2);
        }
    }

    static class FractionUtils {

        // a >= b
        static BigInteger gcd(BigInteger a, BigInteger b)
        {
            if (b.compareTo(BigInteger.ZERO) == 0)
                return a;
            return gcd(b, a.mod(b));
        }


        static Fraction add(Fraction a, Fraction b) {
            BigInteger num = a.num.multiply(b.denom).add(b.num.multiply(a.denom));
            BigInteger denom = a.denom.multiply(b.denom);
            BigInteger gcd;
            if(num.compareTo(denom) > 0) {
                gcd = gcd(num, denom);
            }
            else {
                gcd = gcd(denom, num);
            }
            num = num.divide(gcd);
            denom = denom.divide(gcd);
            return new Fraction(num, denom);
        }

        static Fraction sub(Fraction a, Fraction b) {
            BigInteger num = a.num.multiply(b.denom).subtract(b.num.multiply(a.denom));
            BigInteger denom = a.denom.multiply(b.denom);
            BigInteger gcd;
            if(num.compareTo(denom) > 0) {
                gcd = gcd(num, denom);
            }
            else {
                gcd = gcd(denom, num);
            }
            num = num.divide(gcd);
            denom = denom.divide(gcd);
            return new Fraction(num, denom);
        }

        static Fraction multiply(Fraction a, Fraction b) {
            BigInteger num = a.num.multiply(b.num);
            BigInteger denom = a.denom.multiply(b.denom);
            BigInteger gcd;
            if(num.compareTo(denom) > 0) {
                gcd = gcd(num, denom);
            }
            else {
                gcd = gcd(denom, num);
            }
            num = num.divide(gcd);
            denom = denom.divide(gcd);
            return new Fraction(num, denom);
        }
        static Fraction div(Fraction a, Fraction b) {
            if(a.denom.compareTo(BigInteger.ZERO) == 0 || b.num.compareTo(BigInteger.ZERO) == 0) {
                return null;
            }
            BigInteger num = a.num.multiply(b.denom);
            BigInteger denom = a.denom.multiply(b.num);
            BigInteger gcd;
            if(num.compareTo(denom) > 0) {
                gcd = gcd(num, denom);
            }
            else {
                gcd = gcd(denom, num);
            }
            num = num.divide(gcd);
            denom = denom.divide(gcd);
            return new Fraction(num, denom);
        }

        static Fraction fractionWithDenomAsOne(BigInteger num) {
            return new Fraction(num, BigInteger.ONE);
        }

    }*/

    static class InputReader {
        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 readInt() {
            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 String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        public String next() {
            return readString();
        }
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;
        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }
        public void print(Object...objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }
        public void printLine(Object...objects) {
            print(objects);
            writer.println();
        }
        public void close() {
            writer.close();
        }
        public void flush() {
            writer.flush();
        }
    }
    static class IOUtils {
        public static int[] readIntArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = in.readInt();
            return array;
        }
        static void fillArray(Object o, Object value) {
            if (o.getClass().isArray()) {
                for (int i = 0; i < Array.getLength(o); i++) {
                    if (Array.get(o, i).getClass().isArray()) {
                        fillArray(Array.get(o, i), value);
                    }
                    else {
                        Array.set(o, i, value);
                    }
                }
            }
        }
    }
}