1555_B. Two Tables_137
You have an axis-aligned rectangle room with width W and height H, so the lower left corner is in point (0, 0) and the upper right corner is in (W, H).

There is a rectangular table standing in this room. The sides of the table are parallel to the walls, the lower left corner is in (x_1, y_1), and the upper right corner in (x_2, y_2).

You want to place another rectangular table in this room with width w and height h with the width of the table parallel to the width of the room.

The problem is that sometimes there is not enough space to place the second table without intersecting with the first one (there are no problems with tables touching, though).

You can't rotate any of the tables, but you can move the first table inside the room. 

<image> Example of how you may move the first table.

What is the minimum distance you should move the first table to free enough space for the second one?

Input

The first line contains the single integer t (1 ≤ t ≤ 5000) — the number of the test cases.

The first line of each test case contains two integers W and H (1 ≤ W, H ≤ 10^8) — the width and the height of the room.

The second line contains four integers x_1, y_1, x_2 and y_2 (0 ≤ x_1 < x_2 ≤ W; 0 ≤ y_1 < y_2 ≤ H) — the coordinates of the corners of the first table.

The third line contains two integers w and h (1 ≤ w ≤ W; 1 ≤ h ≤ H) — the width and the height of the second table.

Output

For each test case, print the minimum distance you should move the first table, or -1 if there is no way to free enough space for the second table.

Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}.

Example

Input


5
8 5
2 1 7 4
4 2
5 4
2 2 5 4
3 3
1 8
0 3 1 6
1 5
8 1
3 0 6 1
5 1
8 10
4 5 7 8
8 5


Output


1.000000000
-1
2.000000000
2.000000000
0.000000000

Note

The configuration of the first test case is shown in the picture. But the movement of the first table is not optimal. One of the optimal movement, for example, is to move the table by (0, -1), so the lower left corner will move from (2, 1) to (2, 0). Then you can place the second table at (0, 3)-(4, 5).

In the second test case, there is no way to fit both tables in the room without intersecting.

In the third test case, you can move the first table by (0, 2), so the lower left corner will move from (0, 3) to (0, 5).
import java.text.DecimalFormat;
import java.util.*;
import java.io.*;

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run() {
        boolean tc = true;
        AdityaFastIO r = new AdityaFastIO();
        //FastReader r = new FastReader();

        try (OutputStream out = new BufferedOutputStream(System.out)) {

            //long startTime = System.currentTimeMillis();

            int testcases = tc ? r.ni() : 1;
            int tcCounter = 1;
            // Hold Here Sparky------------------->>>
            // Solution Starts Here

            start:
            while (testcases-- > 0) {

                long W = r.nl();
                long H = r.nl();

                long x1 = r.nl();
                long y1 = r.nl();

                long x2 = r.nl();
                long y2 = r.nl();

                long w = r.nl();
                long h = r.nl();

                DecimalFormat df = new DecimalFormat("0.000000000");
                long ans = 0;
                if (h <= Math.max(H - y2, y1) || w <= Math.max(W - x2, x1))
                    out.write((df.format(ans) + " ").getBytes());
                else {
                    if ((h + (y2 - y1)) <= H) {
                        if ((w + (x2 - x1)) > W) {
                            long max1 = Math.max(H - y2, y1);
                            ans = h - max1;
                            out.write((df.format(ans) + " ").getBytes());
                        } else {
                            long max1 = Math.max(x1, W - x2);
                            long max2 = Math.max(y1, H - y2);
                            ans = Math.min(w - max1, h - max2);
                            out.write((df.format(ans) + " ").getBytes());
                        }
                    } else {
                        if ((w + (x2 - x1)) <= W) {
                            ans = w - Math.max(x1, W - x2);
                            out.write((df.format(ans) + " ").getBytes());
                        } else {
                            out.write((-1 + " ").getBytes());
                        }
                    }
                }
                out.write(("\n").getBytes());
            }
            // Solution Ends Here
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    static class AdityaFastIO {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

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

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

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

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

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // 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 ni() 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 nl() 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 nd() 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();
        }
    }

    public static void main(String[] args) throws Exception {
        run();
    }

    static long mod = 998244353;

    static long modInv(long base, long e) {
        long result = 1;
        base %= mod;
        while (e > 0) {
            if ((e & 1) > 0) result = result * base % mod;
            base = base * base % mod;
            e >>= 1;
        }
        return result;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

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

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

        int ni() {
            return Integer.parseInt(word());
        }

        long nl() {
            return Long.parseLong(word());
        }

        double nd() {
            return Double.parseDouble(word());
        }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1) result = result * x % MOD;
            n = n / 2;
            x = x * x % MOD;
        }
        return result;
    }

    static long powerStrings(int i1, int i2) {
        String sa = String.valueOf(i1);
        String sb = String.valueOf(i2);
        long a = 0, b = 0;
        for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
        for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
        return powerLL(a, b);
    }

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

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long lower_bound(List<Long> list, long k) {
        int s = 0;
        int e = list.size();
        while (s != e) {
            int mid = (s + e) >> 1;
            if (list.get(mid) < k) s = mid + 1;
            else e = mid;
        }
        if (s == list.size()) return -1;
        return s;
    }

    static int upper_bound(List<Long> list, long k) {
        int s = 0;
        int e = list.size();
        while (s != e) {
            int mid = (s + e) >> 1;
            if (list.get(mid) <= k) s = mid + 1;
            else e = mid;
        }
        if (s == list.size()) return -1;
        return s;
    }

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
        graph.get(edge1).add(edge2);
        graph.get(edge2).add(edge1);
    }

    public static class Pair implements Comparable<Pair> {
        long first;
        long second;

        public Pair(long first, long second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if (this.first != o.first)
                return (int) (this.first - o.first);
            else return (int) (this.second - o.second);
        }
    }

    public static class PairC<X, Y> implements Comparable<PairC> {
        X first;
        Y second;

        public PairC(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
        return true;
    }

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
        return true;
    }

}