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.math.*;
import java.io.*; 
 public class C{

static FastReader scan=new FastReader();
 public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
  static LinkedList<Integer>edges[];
  static boolean stdin = true;
    static String filein = "input";
    static String fileout = "output";
static int dx[] = { -1, 0, 1, 0 };
static int dy[] = { 0, 1, 0, -1 };
int dx_8[]={1,1,1,0,0,-1,-1,-1};
int dy_8[]={-1,0,1,-1,1,-1,0,1};
static char sts[]={'U','R','D','L'};
static boolean prime[];
static long LCM(long a,long b){
    return (Math.abs(a*b))/gcd(a,b);
   }
    public static int upperBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = low+(high-low) / 2;
            if ( array[mid]>value) {
                high = mid ;
            } else {
                low = mid+1;
            }
        }
        return low;
    }
   static long gcd(long a, long b) {
    if(a!=0&&b!=0)
        while((a%=b)!=0&&(b%=a)!=0);
    return a^b;
}
static int countSetBits(int n) 
    { 
        int count = 0; 
        while (n > 0) { 
            if((n&1)!=1)
                count++;
            //count += n & 1; 
            n >>= 1; 
        } 
        return count; 
    } 
 static void sieve(long n) 
    { 
        
        prime = new boolean[(int)n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
           
            if(prime[p] == true) 
            { 
                
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
    }  
  
 
 
           static boolean isprime(long x)
           {
            for(long i=2;i*i<=x;i++)
                if(x%i==0)
                    return false;
                return true;
           }
           static int perm=0,FOR=0;
           
     

static boolean flag=false;
static int len=100000000;

static ArrayList<Pair>inters=new ArrayList<Pair>();





static StringBuilder sb;
static void swap(int i,int j,StringBuilder st)
{
    char tmp=st.charAt(i);
    st.setCharAt(i,st.charAt(j));
    st.setCharAt(j,tmp);
}


 private static int next(int[] arr, int target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to right side if target is  
            // greater.  
            if(arr[mid]==target)
                return mid;
            if (arr[mid] <target) {  
                start = mid + 1;  
            }  
    
            // Move left side.  
            else {  
                ans = mid;  
                end = mid - 1;  
            }  
        }  
        return ans;  
    }  
//static boolean vis[][];
    static long solve(int h,long n,int cur)
    {
        if(h==0)
            return 0;
        long half=1L<<(h-1);
        if(n<=half)
        {
            if((cur^1)==0)
                return 1+solve(h-1,n,0);
            else 
                return 2*half+solve(h-1,n,0);
        }
        else 
        {
              if((cur^1)==0)
             return 2*half+solve(h-1,n-half,1);
            else 
                return 1+solve(h-1,n-half,1);
        }
    }

  
public static class comp1 implements Comparator<String>{  
public int compare(String o1,String o2){
return o1.length()-o2.length(); 
}
  }
  public static class comp2 implements Comparator<String>{  
public int compare(String o1,String o2){
return o1.compareTo(o2); 
}
  }
  static StringBuilder a,b;

    static boolean isPowerOfTwo(int n)
{
    if(n==0)
    return false;
 
return (int)(Math.ceil((Math.log(n) / Math.log(2)))) == 
       (int)(Math.floor(((Math.log(n) / Math.log(2)))));
}
static ArrayList<Integer>v;
static ArrayList<Integer>pows;
static void block(long x) 
{ 
   v = new ArrayList<Integer>(); 
      
    pows=new ArrayList<Integer>();
   
    while (x > 0)  
    { 
        v.add((int)x % 2); 
        x = x / 2; 
    } 
  
    // Displaying the output when 
    // the bit is '1' in binary 
    // equivalent of number. 
    for (int i = 0; i < v.size(); i++)  
    { 
        if (v.get(i)==1)  
        { 
      pows.add(i); 
        } 
    } 

} 


   static long mod=(long)(1e9)+7;
    static int countWaysUtil(int x, int n, int num) 
    { 
        // Base cases 
        int val = (int) (x - Math.pow(num, n)); 
        if (val == 0) 
            return 1; 
        if (val < 0) 
            return 0; 
       
        // Consider two possibilities, num is 
        // included and num is not included. 
        return countWaysUtil(val, n, num + 1) + 
               countWaysUtil(x, n, num + 1); 
    }
       static int countWays(int x, int n) 
    { 
        return countWaysUtil(x, n, 1); 
    } 
   
        
        static ArrayList<Integer>arr;
        static int n,k;
        static int dp[][];
        static int rec(int l,int r,int i,int j)
        {
            if(i>j)
            {
                if(r-l>k)
                    return (int)1e7+5;

                return 0;
            }
             if(r-l<=k)
                return 0;
            int x=(int)1e7+5;
            if(dp[l][r]!=-1)
                return dp[l][r];
            if(arr.get(i)-l<=k)
            {
                return x=Math.min(rec(arr.get(i),r,i+1,j)+1,rec(l,r,i+1,j));
            }
            else if(r-arr.get(j)<=k)
            {
                x=Math.min(rec(l,arr.get(j),i,j-1)+1,rec(l,r,i,j-1));
            }

            return dp[l][r]=x;
        }
       
public static void main(String[] args)  throws Exception 
{
//SUCK IT UP AND DO IT ALRIGHT
//scan=new FastReader("div7.in");
//out = new PrintWriter("div7.out");
   //System.out.println(countSetBits(2015));
    //int elem[]={1,2,3,4,5};
//System.out.println("avjsmlfpb".compareTo("avjsmbpfl"));
int tt=1;
tt=scan.nextInt();
//String ok="ABDC";
//System.out.println(ok.substring(2));
//System.out.println(2000000000/2);
//tt=scan.nextInt();
//System.out.println(isprime(23335));
//int T=1;
  outer:while(tt-->0)
 {
 int n=scan.nextInt(),l=scan.nextInt();
 int arr[]=new int[n];
 for(int i=0;i<n;i++)
    arr[i]=scan.nextInt();
double lspeed=1,rspeed=1,lplace=0,rplace=l;
int ll=0,rr=n-1;
double res=0;
while(true)
{
    if(ll>rr)
    {
        //out.println("FUCK");
        res+=(rplace-lplace)/(lspeed+rspeed);
        break;
    }
   /* else if(ll==rr)
    {
        //out.println(res);
        double dis=(rplace-arr[rr])/rspeed,dis2=(arr[ll]-lplace)/lspeed;
        if(Double.compare(dis,dis2)<0)
        {
         //   out.println("FUCK");
           res+=dis;
            rplace=arr[rr];
            lplace+=(rplace-arr[rr]);
            rspeed++;
           res+=(rplace-lplace)/(lspeed+rspeed);
        }
        else if(Double.compare(dis,dis2)>0)
        {
           // out.println("FUCK");
          //  res+=dis;
            res+=dis2;
            rplace-=(arr[ll]-lplace);
            lplace=arr[ll];
            lspeed++;
           // out.println(rplace+" "+lplace+" "+res);
res+=(rplace-lplace)/(lspeed+rspeed);
        }
        else 
        {
     //       out.println(rspeed+" "+l);
            res+=(rplace-lplace)/(lspeed+rspeed);

        }
        break;
    }*/
double ltime=(arr[ll]-lplace)/lspeed;
double rtime=(rplace-arr[rr])/rspeed;
if(Double.compare(ltime,rtime)<0)
{
    //out.println("FUCK");
    res+=ltime;
    lplace=arr[ll];
    rplace-=(ltime*rspeed);
    ll++;
    lspeed++;
}
else
{
    //out.println("FUCK");
    res+=rtime;
    rplace=arr[rr];
    lplace+=(rtime*lspeed);
   //System.out.printf("%.10f\n",rplace);
   //System.out.printf("%.10f\n",lplace);

    rr--;
    rspeed++;
}
/*else 
{
res+=ltime;
rplace=arr[rr];
lplace=arr[ll];
lspeed++;
rspeed++;
ll++;
rr--;    
}*/
}
 out.println(String.format("%.10f", res));
   

}
out.close();

//SEE UP 

}
static class special{
    char c;
    int idx;
    special(char c,int idx)
    {
        this.c=c;
        this.idx=idx;
    }
}
static long binexp(long a,long n)
{
    if(n==0)
        return 1;
    long res=binexp(a,n/2);
    if(n%2==1)
        return res*res*a;
    else 
        return res*res;
}
static long fastPow(int base, int pow) {
        if (pow==0)
            return 1;
        long half=fastPow(base, pow/2);
        if (pow%2==0)
            return half*half%mod;
        return half*half%mod*base%mod;
    }
static long powMod(long base, long exp, long mod) {
       if (base == 0 || base == 1) return base;
       if (exp == 0) return 1;
       if (exp == 1) return (base % mod+mod)%mod;
       long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
       R *= R;
       R %= mod;
       if ((exp & 1) == 1) {
           return (base * R % mod+mod)%mod;
       }
       else return (R %mod+mod)%mod;
   }
static double dis(double x1,double y1,double x2,double y2)
{
    return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
static long mod(long x,long y)
    {
        if(x<0)
            x=x+(-x/y+1)*y;
        return x%y;
    }
 public static  long pow(long b, long e) {
            long r = 1;
            while (e > 0) {
                if (e % 2 == 1) r = r * b ;
                b = b * b;
                e >>= 1;
            }
            return r;
        }
private static void sort(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
    //Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
private static void sort2(int[] arr) {
        List<Integer> list = new ArrayList<>();
        for (int object : arr) list.add(object);
        Collections.sort(list);
    Collections.reverse(list);
        for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
    }
 public static class FastReader {
        BufferedReader br;
        StringTokenizer root;
        
 
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        FastReader(String filename)throws Exception
        {

            br=new BufferedReader(new FileReader(filename));
        }

        boolean hasNext(){
            String line;
            while(root.hasMoreTokens())
                return true;
            return false;
        }
 
        String next() {
            while (root == null || !root.hasMoreTokens()) {
                try {
                    root = new StringTokenizer(br.readLine());
                } catch (Exception addd) {
                    addd.printStackTrace();
                }
            }
            return root.nextToken();
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
 
        long nextLong() {
            return Long.parseLong(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception addd) {
                addd.printStackTrace();
            }
            return str;
        }
         public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }
 
            return array;
        }
}
 static class Pair implements Comparable<Pair>{
        public long x, y;
        public Pair(long x1, long y1) {
            x=x1;
            y=y1;
        }
        @Override
        public int hashCode() {
            return (int)(x + 31 * y);
        }
        public String toString() {
            return x + " " + y;
        }
        @Override
        public boolean equals(Object o){
            if (o == this) return true;
            if (o.getClass() != getClass()) return false;
            Pair t = (Pair)o;
            return t.x == x && t.y == y;
        }
public int compareTo(Pair o)
{
    return (int)(o.y-y);

    }

}
 static class tuple{
        int x,y,z;
        tuple(int a,int b,int c){
            x=a;
            y=b;
            z=c;
        }
    }
    static class Edge{
        int d,w;
        Edge(int d,int w)
        {
            this.d=d;
            this.w=w;
        }
    }
}