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.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author ilyakor
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskE1 solver = new TaskE1();
    int testCount = Integer.parseInt(in.next());
    for (int i = 1; i <= testCount; i++) {
      solver.solve(i, in, out);
    }
    out.close();
  }

  static class TaskE1 {

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      int m = in.nextInt();
      // int n = 12;
      // int m = 2000;
      int[][] d = new int[2][1 << n];
      int[] buf = new int[1 << n];
      int[][] a = new int[m][n];
      for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
          a[j][i] = in.nextInt();
          // a[j][i] = (int)((i * 12346L + j * 789L) % 100000);
        }
      }

      ArrayList<Integer> inds = new ArrayList<>();
      for (int i = 0; i < m; ++i) {
        inds.add(i);
      }
      int[][] finalA = a;
      Collections.sort(inds, new Comparator<Integer>() {

        public int compare(Integer i1, Integer i2) {
          int val1 = 0, val2 = 0;
          for (int i = 0; i < n; ++i) {
            if (finalA[i1][i] > val1) {
              val1 = finalA[i1][i];
            }
          }
          for (int i = 0; i < n; ++i) {
            if (finalA[i2][i] > val2) {
              val2 = finalA[i2][i];
            }
          }
          return -Integer.compare(val1, val2);
        }
      });
      int newM = Math.min(m, n + 1);
      int[][] na = new int[newM][];
      for (int i = 0; i < newM; ++i) {
        int ind = inds.get(i);
        na[i] = a[ind];
      }
      m = newM;
      a = na;

      for (int i = 0; i < m; ++i) {
        int[] prev = d[i % 2], nx = d[(i + 1) % 2];
        for (int shift = 0; shift < n; ++shift) {
          int[] b = new int[n];
          for (int j = 0; j < n; ++j) {
            b[j] = a[i][(j + shift) % n];
          }
          System.arraycopy(prev, 0, buf, 0, prev.length);
          for (int j = 0; j < n; ++j) {
            int inc = b[j];
            for (int mask = 0; mask < (1 << n); ++mask) {
              if ((mask >> j) % 2 == 0) {
                int val = buf[mask] + inc;
                int nm = mask ^ (1 << j);
                if (val > buf[nm]) {
                  buf[nm] = val;
                }
              }
            }
          }
          for (int mask = 0; mask < (1 << n); ++mask) {
            if (nx[mask] < buf[mask]) {
              nx[mask] = buf[mask];
            }
          }
        }
      }
      out.printLine(d[m % 2][(1 << n) - 1]);
    }

  }

  static class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void printLine(Object... objects) {
      print(objects);
      writer.println();
    }

    public void close() {
      writer.close();
    }

  }

  static class InputReader {

    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

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

    public static boolean isSpace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
      if (count == -1) {
        throw new InputMismatchException();
      }
      try {
        if (cur >= count) {
          cur = 0;
          count = stream.read(buffer);
          if (count <= 0) {
            return -1;
          }
        }
      } catch (IOException e) {
        throw new InputMismatchException();
      }
      return buffer[cur++];
    }

    public int readSkipSpace() {
      int c;
      do {
        c = read();
      } while (isSpace(c));
      return c;
    }

    public String nextToken() {
      int c = readSkipSpace();
      StringBuilder sb = new StringBuilder();
      while (!isSpace(c)) {
        sb.append((char) c);
        c = read();
      }
      return sb.toString();
    }

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

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

  }
}