Problem: This is a harder version of the problem. The difference is only in constraints.

You are given a rectangular n × m matrix a. In one move you can choose any column and cyclically shift elements in this column. You can perform this operation as many times as you want (possibly zero). You can perform this operation to a column multiple times.

After you are done with cyclical shifts, you compute for every row the maximal value in it. Suppose that for i-th row it is equal r_i. What is the maximal possible value of r_1+r_2+…+r_n?

Input

The first line contains an integer t (1 ≤ t ≤ 40), the number of test cases in the input.

The first line of each test case contains integers n and m (1 ≤ n ≤ 12, 1 ≤ m ≤ 2000) — the number of rows and the number of columns in the given matrix a. 

Each of the following n lines contains m integers, the elements of a (1 ≤ a_{i, j} ≤ 10^5).

Output

Print t integers: answers for all test cases in the order they are given in the input.

Example

Input


3
2 3
2 5 7
4 2 4
3 6
4 1 5 2 10 4
8 6 6 4 9 10
5 4 9 5 8 7
3 3
9 9 9
1 1 1
1 1 1


Output


12
29
27

Note

In the first test case you can shift the third column down by one, this way there will be r_1 = 5 and r_2 = 7.

In the second case you can don't rotate anything at all, this way there will be r_1 = r_2 = 10 and r_3 = 9.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        E2RotateColumnsHardVersion solver = new E2RotateColumnsHardVersion();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class E2RotateColumnsHardVersion {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            E2RotateColumnsHardVersion.Column[] columns = new E2RotateColumnsHardVersion.Column[m];
            for (int i = 0; i < columns.length; ++i) columns[i] = new E2RotateColumnsHardVersion.Column(new int[n]);
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    columns[j].v[i] = in.nextInt();
                    if (i == n - 1) columns[j].initMax();
                }
            }
            Arrays.sort(columns, new Comparator<E2RotateColumnsHardVersion.Column>() {

                public int compare(E2RotateColumnsHardVersion.Column o1, E2RotateColumnsHardVersion.Column o2) {
                    return o2.max - o1.max;
                }
            });
            if (columns.length > n)
                columns = Arrays.copyOf(columns, n);

            long[] dp = new long[1 << n];
            for (E2RotateColumnsHardVersion.Column c : columns) {
                long[] ndp = new long[1 << n];
                System.arraycopy(dp, 0, ndp, 0, dp.length);

                for (int rot = 0; rot < n; ++rot) {
                    long[] temp = new long[1 << n];
                    System.arraycopy(dp, 0, temp, 0, dp.length);
                    for (int i = 0, pos = rot; i < n; ++i, ++pos) {
                        if (pos >= n) pos = 0;
                        int val = c.v[pos];
                        for (int j = 0; j < temp.length; ++j) {
                            if ((j & (1 << i)) == 0)
                                temp[j | (1 << i)] = Math.max(temp[j | (1 << i)], temp[j] + val);
                        }
                    }
                    for (int i = 0; i < ndp.length; ++i)
                        ndp[i] = Math.max(ndp[i], temp[i]);
                }
                dp = ndp;
            }
            out.println(dp[dp.length - 1]);
        }

        static class Column {
            int[] v;
            int max;

            public Column(int[] v) {
                this.v = v;
            }

            void initMax() {
                max = 0;
                for (int vv : v) max = Math.max(max, vv);
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public String next() {
            return nextString();
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = pread();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}