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.*;

public class Solution {
    public static class Node implements Comparable<Node> {
        int ind = -1;
        int val = -1;

        public Node(int ind, int val) {
            this.ind = ind;
            this.val = val;
        }

        public int compareTo(Node node) {
            if (this.val > node.val) {
                return 1;
            } else if (this.val < node.val){
                return -1;
            }
            else{
                return 0;
            }
        }
    }

    public static int cycles = 0;

    public static int[] nextArray(FastReader sc1, int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc1.nextInt();
        }
        return arr;
    }

    public static int max1 = 0;

    public static int check_left(int st, int en, int[] arr, int val){
        if(st <= en){
            int mid = (st+en)/2;
            if(mid==(arr.length-1) && arr[mid]<=val){
                return mid;
            }
            if(val>=arr[mid] && val<arr[mid+1]){
                return mid;
            }
            else if(val>arr[mid]){
                return check_left(mid+1, en, arr, val);
            }
            else{
                return check_left(st, mid-1, arr, val);
            }
        }
        return -1;
    }

    public static int check_right(int st, int en, int[] arr, int val){
        if(st <= en){
            int mid = (st+en)/2;
            if(mid==0 && arr[mid]>=val){
                return mid;
            }
            if(val<=arr[mid] && val>arr[mid-1]){
                return mid;
            }
            else if(val>arr[mid]){
                return check_right(mid+1, en, arr, val);
            }
            else{
                return check_right(st, mid-1, arr, val);
            }
        }
        return -1;
    }

    public static double compute_val(int st,int en,int[] arr,double[] tim1,int[] vel1, double[] tim2, int[] vel2,int n, int l){
        if(st <= en){
            int mid = (st+en)/2;
            int ln = check_left(0,n-1,arr,mid);
            int rn = check_right(0,n-1,arr,mid);

            double time1 = 0.0;
            double time2 = 0.0;

            if(ln != -1 ){
                int dist1 = mid - arr[ln];
                time1 = tim1[ln] + (double)dist1/vel1[ln];
            }
            else{
                time1 = (double)mid;
            }

            if(rn != -1){
                int dist2 = arr[rn] - mid;
                time2 = tim2[rn] + (double)dist2/vel2[rn];
            }
            else{
                time2 = (double)l-(double)mid;
            }

            System.out.println(time1+" "+time2);
            if(Math.abs(time1-time2) <= 0.000001){
                return time1;
            }

            if(time1 < time2){
                return compute_val(mid+1, en, arr, tim1, vel1, tim2, vel2, n, l);
            }
            else{
                return compute_val(st, mid-1, arr, tim1, vel1, tim2, vel2, n, l);
            }
        }
        return 0.0;
    }
    public static void main(String[] args) {
        FastReader sc1 = new FastReader();
        StringBuilder sb = new StringBuilder();

        int tc = sc1.nextInt();
        int ch = 0;

        while(ch<tc){
            int n = sc1.nextInt();
            int l = sc1.nextInt();
            int[] arr = nextArray(sc1, n);
            double[] tim1 = new double[n];
            int[] vel1 = new int[n];
            double[] tim2 = new double[n];
            int[] vel2 = new int[n];
            
            for(int i=0; i<n; i++){
                vel1[i] = i==0 ? 2: vel1[i-1]+1;
                int dist = i==0 ? arr[i] : arr[i] - arr[i-1];
                tim1[i] = i==0 ? (double)dist/1.0 : tim1[i-1] + ((double)dist)/(double)vel1[i-1]; 
            }

            for(int i=n-1; i>=0; i--){
                vel2[i] = i==(n-1) ? 2: vel2[i+1]+1;
                
                double d1 = (double)l-(double)arr[i];         

                double dist = i==(n-1) ? d1 : ((double)arr[i+1] - (double)arr[i]);
                tim2[i] = i==(n-1) ? d1/1.0 : tim2[i+1] + dist/(double)vel2[i+1]; 
            }

            int cpoint = -1;
            for(int i=0; i<n; i++){
                if(tim1[i] >= tim2[i]){
                    cpoint = i;
                    break;
                }
            }

            double rtime = 0.0;

            if(cpoint > 0){
                double timea = tim1[cpoint-1];
                double timeb = tim2[cpoint];
                double dista = arr[cpoint-1];
                double distb = arr[cpoint];
                if(timea < timeb){
                    dista += (double)vel1[cpoint-1]*(timeb-timea);
                }
                else{
                    distb -= (double)vel2[cpoint]*(timea-timeb);
                }

                rtime = Math.max(timea, timeb) + (distb-dista)/((double)vel1[cpoint-1]+(double)vel2[cpoint]);
            }
            else if(cpoint == 0){
                double timea = 0;
                double timeb = tim2[cpoint];
                double dista = 0.0;
                double distb = arr[cpoint];
                if(timea < timeb){
                    dista += (double)1.0*(timeb-timea);
                }
                else{
                    distb -= (double)vel2[cpoint]*(timea-timeb);
                }

                rtime = Math.max(timea, timeb) + (distb-dista)/((double)1.0+(double)vel2[cpoint]);
            }
            else if(cpoint == -1){
                double timea = tim1[n-1];
                double timeb = 0;
                double dista = arr[n-1];
                double distb = l;
                if(timea < timeb){
                    dista += (double)vel1[n-1]*(timeb-timea);
                }
                else{
                    distb -= (double)1.0*(timea-timeb);
                }

                rtime = Math.max(timea, timeb) + (distb-dista)/((double)vel1[n-1]+(double)1.0);
            }

            String ans = String.format("%.8f", rtime);
            sb.append(ans+"\n");
            ch++;
        }

        System.out.print(sb.toString());
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

}