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.util.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.MathContext;
public class Main {
    static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }
    
    public static void sort(int arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(int arr[],int l1,int r1,int l2,int r2) {
        int tmp[]=new int[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    public static void sort(long arr[],int l,int r) {    //sort(arr,0,n-1);
        if(l==r) {
            return;
        }
        int mid=(l+r)/2;
        sort(arr,l,mid);
        sort(arr,mid+1,r);
        merge(arr,l,mid,mid+1,r);
    }
    public static void merge(long arr[],int l1,int r1,int l2,int r2) {
        long tmp[]=new long[r2-l1+1];
        int indx1=l1,indx2=l2;
        //sorting the two halves using a tmp array
        for(int i=0;i<tmp.length;i++) {
            if(indx1>r1) {
                tmp[i]=arr[indx2];
                indx2++;
                continue;
            }
            if(indx2>r2) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            if(arr[indx1]<arr[indx2]) {
                tmp[i]=arr[indx1];
                indx1++;
                continue;
            }
            tmp[i]=arr[indx2];
            indx2++;
        }
        //Copying the elements of tmp into the main array
        for(int i=0,j=l1;i<tmp.length;i++,j++) {
            arr[j]=tmp[i];
        }
    }
    
    public static void main(String args[]) throws IOException {
        Scan input=new Scan();
        StringBuilder ans=new StringBuilder("");
        int test=input.scanInt();
        for(int tt=1;tt<=test;tt++) {
            int n=input.scanInt()+2;
            int l=input.scanInt();
            int arr[]=new int[n];
            for(int i=1;i<n-1;i++) {
                arr[i]=input.scanInt();
            }
            arr[n-1]=l;
            ans.append(solve(n,arr)+"\n");
        }
        System.out.println(ans);
    }
    public static String solve(int n,int arr[]) {
        int speed=1;
        BigDecimal time_l[]=new BigDecimal[n];
        BigDecimal time=new BigDecimal("0");
        time_l[0]=new BigDecimal("0");
        for(int i=1;i<n;i++) {
            int dist=arr[i]-arr[i-1];
            BigDecimal tmp=new BigDecimal(""+dist).divide(new BigDecimal(""+speed), MathContext.DECIMAL64);
            time=time.add(tmp,MathContext.DECIMAL64);
            time_l[i]=new BigDecimal(""+time);
            speed++;
        }
        speed=1;
        BigDecimal time_r[]=new BigDecimal[n];
        time_r[n-1]=new BigDecimal("0");
        time=new BigDecimal("0");
        for(int i=n-2;i>=0;i--) {
            int dist=arr[i+1]-arr[i];
            BigDecimal tmp=new BigDecimal(""+dist).divide(new BigDecimal(""+speed), MathContext.DECIMAL64);
            time=time.add(tmp,MathContext.DECIMAL64);
            time_r[i]=new BigDecimal(""+time);
            speed++;
        }
        for(int i=0;i<n;i++) {
            if(time_l[i].compareTo(time_r[i])==0) {
                return ""+time_l[i];
            }
        }
//        for(int i=0;i<n;i++) {
//            System.out.print(time_l[i]+"\t");
//        }
//        System.out.println();
//        for(int i=0;i<n;i++) {
//            System.out.print(time_r[i]+"\t");
//        }
//        System.out.println();
        for(int i=0;i<n-1;i++) {
            if(time_l[i].compareTo(time_r[i])==-1 && time_l[i+1].compareTo(time_r[i+1])==1) {
                BigDecimal sub=new BigDecimal("0");
//                System.out.println("cmp "+time_l[i]+" "+time_r[i]+" "+time_l[i].compareTo(time_r[i+1]));
                if(time_l[i].compareTo(time_r[i+1])==-1) {
                    BigDecimal diff=time_r[i+1].subtract(time_l[i]);
                    time_l[i]=time_l[i].add(diff, MathContext.DECIMAL64);
                    int speed_l=1+i;
                    sub=new BigDecimal(""+speed_l).multiply(diff, MathContext.DECIMAL64);
                }
                else if(time_l[i].compareTo(time_r[i+1])==1){
                    BigDecimal diff=time_l[i].subtract(time_r[i+1]);
                    int speed_r=1+(n-i-2);
                    sub=new BigDecimal(""+speed_r).multiply(diff, MathContext.DECIMAL64);
                }
                int speed_l=1+i;
                int speed_r=1+(n-i-2);
                speed=speed_l+speed_r;
                BigDecimal dist=new BigDecimal(""+(arr[i+1]-arr[i]));
                dist=dist.subtract(sub);
                BigDecimal tmp=new BigDecimal(""+dist).divide(new BigDecimal(""+speed), MathContext.DECIMAL64);
                time_l[i]=time_l[i].add(tmp,MathContext.DECIMAL64);
                return ""+time_l[i];
            }
        }
        BigDecimal cmp=new BigDecimal("0.000001");
        for(int i=0;i<n;i++) {
            BigDecimal diff=time_l[i].subtract(time_r[i], MathContext.DECIMAL64);
            diff=diff.abs();
            if(diff.compareTo(cmp)==-1 || diff.compareTo(cmp)==0) {
                return ""+time_l[i];
            }
        }
        return "11";
    }
}