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.io.IOException;
    import java.math.BigInteger;
    import java.util.*;





        //import javafx.util.Pair; 
        //import java.util.concurrent.LinkedBlockingDeque;







            
         public class Codeforces {
            
                
                public static long mod = 1000000007 ;
                public static double epsilon=0.00000000008854;//value of epsilon
                public static InputReader sc = new InputReader(System.in);
                public static PrintWriter pw = new PrintWriter(System.out);
                
                public static long pow(long x,long y,long mod){
                    long ans=1;
                    
                    x%=mod;
                    while(y>0){
                        if((y&1)==1){
                            ans=(ans*x)%mod;
                        }
                        y=y>>1;
                        x=(x*x)%mod;
                    }
                    return ans;
                }
                public static ArrayList<ArrayList <Pair>> GetGraph(int n,int m,HashSet<Integer> h){
                    ArrayList<ArrayList <Pair>> a=new ArrayList<>();
                    for(int i=0;i<n;i++){
                        a.add(new ArrayList<>());
                    }
                    for(int i=0;i<m;i++){
                        int u=sc.nextInt()-1;
                        int v=sc.nextInt()-1;
                        if(h.contains(v)){
                            h.remove(v);
                        }
                        a.get(u).add(new Pair(v, 0));
                        //a.get(v).add(new Pair(u, 1));
                    } 
                    return a;
                }
               
                public static int firstNode(int a,int p[]){
                    if(a!=p[a]){
                        p[a]=firstNode(p[a], p);
                    }
                    return p[a];
                }
                public static void Union(int a,int b,int p[]){
                    //int a=firstNode(a1, p);
                    //int b=firstNode(b1, p);
                    /*if(a!=b){
                        if(r[a]<r[b]){
                            p[a]=b;
                        }
                        else if(r[a]>r[b]){
                            p[b]=a;
                        }
                        else{
                            r[b]++;
                            p[a]=b;
                        }
                    }*/
                    if(a!=b)
                    p[firstNode(a,p)]=firstNode(b,p);//if no rank than 
                }
            
               public static boolean check(double time,int a[],int l){
                   double start=0,dis=0,speed=1,end=l;
                   int n=a.length;
                   double f=time;
                   for(int i=0;i<n;i++){
                    dis=a[i]-dis;
                    double to=dis/speed;
                    if(to>=time){
                        start+=speed*time;
                        time=0;
                        break;
                    }
                    else{
                        start=a[i];
                        time-=to;
                        speed++;
                    }
                    dis=a[i];
                   }
                   start+=speed*time;
                   dis=l;time=f;speed=1;
                   for(int i=n-1;i>=0;i--){
                    dis=dis-a[i];
                    double to=dis/speed;
                    if(to>=time){
                        end-=speed*time;
                        time=0;
                        break;
                    }
                    else{
                        end=a[i];
                        time-=to;
                        speed++;
                    }
                    dis=a[i];
                   }
                   end-=speed*time;
                   if(start>=end){
                       return true;
                   }
                   else{
                       return false;
                   }
               }
                public static void main(String[] args) throws Exception {
                    // code starts.
                    int q=sc.nextInt();
                   while(q-->0){
                       int n=sc.nextInt();
                       int end=sc.nextInt();
                       int a[]=scanArray(n);
                       double l=0,r=end,ans=-1;
                       for(int i=0;i<100;i++){
                        double mid=(l+r)/2;
                        if(check(mid, a, end)){
                            r=mid;
                            ans=mid;
                        }
                        else l=mid;
                       }
                       pw.printf("%.8f\n",ans);

                    
                   }
                   
                    // Code ends...
                    pw.flush();
                    pw.close();
                }
                public static Comparator<Integer[]> MOquery(int block){
                    return
                    new Comparator<Integer[]>(){
                        @Override
                        public int compare(Integer a[],Integer b[]){
                            int a1=a[0]/block;
                            int b1=b[0]/block;
                            if(a1==b1){
                                if((a1&1)==1)
                                return a[1].compareTo(b[1]);
                                else{
                                    return b[1].compareTo(a[1]);
                                }
                            }
                            return a1-b1;
                        }
                    };
                }
            
                public static Comparator<Long[]> column(int i){
                    return 
                    new Comparator<Long[]>() {
                        @Override
                        public int compare(Long[] o1, Long[] o2) {
                            return o1[i].compareTo(o2[i]);//for ascending
                            //return o2[i].compareTo(o1[i]);//for descending
                        }
                    };
                }
                public static Comparator<Integer[]> column(){
                    return 
                    new Comparator<Integer[]>() {
                        @Override
                        public int compare(Integer[] o1, Integer[] o2) {
                            //return o1[i].compareTo(o2[i]);//for ascending
                            //return o2[i].compareTo(o1[i]);//for descending
                            long a1=o1[0];
                            long a2=o2[1];
                            long b1=o2[0];
                            long b2=o1[1];
                            int ans=0;
                            if(a1*a2>b1*b2){
                                ans=1;
                            }
                            else ans=-1;
                            return ans;
                        }
                    };
                }
                public static Comparator<Integer[]> col(int i){
                    return 
                    new Comparator<Integer[]>() {
                        @Override
                        public int compare(Integer[] o1, Integer[] o2) {
                            if(o1[i]-o2[i]!=0)
                            return o1[i].compareTo(o2[i]);//for ascending
                            return o1[i+1].compareTo(o2[i+1]);
                            //return o2[i].compareTo(o1[i]);//for descending
                        }
                    };
                }
                public static Comparator<Integer> des(){
                    return 
                    new Comparator<Integer>() {
                        @Override
                        public int compare(Integer o1, Integer o2) {
                            //return o1[i].compareTo(o2[i]);//for ascending
                            return o2.compareTo(o1);//for descending
                        }
                    };
                }
                
                
                
                
                public static String reverseString(String s){
                    StringBuilder input1 = new StringBuilder(); 
                    input1.append(s);  
                    input1 = input1.reverse();
                    return input1.toString();
                }
                public static int[] scanArray(int n){
                    int a[]=new int [n];
                    //Random x=new Random();
                    for(int i=0;i<n;i++){
                        a[i]=sc.nextInt();
                    }
                    
            
                    return a;
                }
                public static long[] scanLongArray(int n){
                    long a[]=new long [n];
                    for(int i=0;i<n;i++)
                    a[i]=sc.nextLong();
            
                    return a;
                }
                public static String [] scanStrings(int n){
                    String a[]=new String [n];
                    for(int i=0;i<n;i++)
                    a[i]=sc.nextLine();
            
                    return a;
                }
                public static class InputReader {
            
                    private final InputStream stream;
                    private final byte[] buf = new byte[8192];
                    private int curChar, snumChars;
                    private SpaceCharFilter filter;
            
                    public InputReader(InputStream stream) {
                        this.stream = stream;
                    }
            
                    public int snext() {
                        if (snumChars == -1)
                            throw new InputMismatchException();
                        if (curChar >= snumChars) {
                            curChar = 0;
                            try {
                                snumChars = stream.read(buf);
                            } catch (IOException e) {
                                throw new InputMismatchException();
                            }
                            if (snumChars <= 0)
                                return -1;
                        }
                        return buf[curChar++];
                    }
            
                    public int nextInt() {
                        int c = snext();
                        while (isSpaceChar(c)) {
                            c = snext();
                        }
                        int sgn = 1;
                        if (c == '-') {
                            sgn = -1;
                            c = snext();
                        }
                        int res = 0;
                        do {
                            if (c < '0' || c > '9')
                                throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                        } while (!isSpaceChar(c));
                        return res * sgn;
                    }
            
                    public long nextLong() {
                        int c = snext();
                        while (isSpaceChar(c)) {
                            c = snext();
                        }
                        int sgn = 1;
                        if (c == '-') {
                            sgn = -1;
                            c = snext();
                        }
                        long res = 0;
                        do {
                            if (c < '0' || c > '9')
                                throw new InputMismatchException();
                            res *= 10;
                            res += c - '0';
                            c = snext();
                        } while (!isSpaceChar(c));
                        return res * sgn;
                    }
            
                    public int[] nextIntArray(int n) {
                        int a[] = new int[n];
                        for (int i = 0; i < n; i++) {
                            a[i] = nextInt();
                        }
                        return a;
                    }
            
                    public String readString() {
                        int c = snext();
                        while (isSpaceChar(c)) {
                            c = snext();
                        }
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = snext();
                        } while (!isSpaceChar(c));
                        return res.toString();
                    }
            
                    public String nextLine() {
                        int c = snext();
                        while (isSpaceChar(c))
                            c = snext();
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = snext();
                        } while (!isEndOfLine(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;
                    }
            
                    private boolean isEndOfLine(int c) {
                        return c == '\n' || c == '\r' || c == -1;
                    }
            
                    public interface SpaceCharFilter {
                        public boolean isSpaceChar(int ch);
                    }
                }
                
            }
            
            class SparseTable{
                int p[][];
                int log[];
                SparseTable(int a[]){
                    log=new int[a.length];
                    for(int i=2;i<a.length;i++){
                        log[i]=log[i/2]+1;
                    }
                    p=new int[a.length][25];
                    
                    for(int i=0;i<a.length;i++){
                        p[i][0]=a[i];
                    }
                    
                    build(p);
                    //System.out.println(Arrays.toString(log));
                }
                void build(int p[][]){
                    for(int h=1;h<25;h++){
                        for(int i=0;i+(1<<(h-1))<p.length;i++){
                            p[i][h]=compare(p[i][h-1], p[i+(1<<(h-1))][h-1]);
                        }
                    }
                }
                int getO1(int l,int r){
                    int k=log[r-l+1];
                    
                        return compare(p[l][k],p[r-(1<<k)+1][k]);
                    
                }
                int compare(int a,int b){
                    return Math.max(a, b);
                }
            }
            class Pair{
                int v,w;
                Pair(int node,int weight){
                    v=node;
                    w=weight;
                }
            }