description: It is the hard version of the problem. The only difference is that in this version 1 ≤ n ≤ 300.
  
  In the cinema seats can be represented as the table with n rows and m columns. The rows are numbered with integers from 1 to n. The seats in each row are numbered with consecutive integers from left to right: in the k-th row from m (k - 1) + 1 to m k for all rows 1 ≤ k ≤ n.
  
  1| 2| ⋅⋅⋅| m - 1| m  
  ---|---|---|---|---  
  m + 1| m + 2| ⋅⋅⋅| 2 m - 1| 2 m  
  2m + 1| 2m + 2| ⋅⋅⋅| 3 m - 1| 3 m  
  \vdots| \vdots| \ddots| \vdots| \vdots  
  m (n - 1) + 1| m (n - 1) + 2| ⋅⋅⋅| n m - 1| n m  
  The table with seats indices
  
  There are nm people who want to go to the cinema to watch a new film. They are numbered with integers from 1 to nm. You should give exactly one seat to each person.
  
  It is known, that in this cinema as lower seat index you have as better you can see everything happening on the screen. i-th person has the level of sight a_i. Let's define s_i as the seat index, that will be given to i-th person. You want to give better places for people with lower sight levels, so for any two people i, j such that a_i < a_j it should be satisfied that s_i < s_j.
  
  After you will give seats to all people they will start coming to their seats. In the order from 1 to nm, each person will enter the hall and sit in their seat. To get to their place, the person will go to their seat's row and start moving from the first seat in this row to theirs from left to right. While moving some places will be free, some will be occupied with people already seated. The inconvenience of the person is equal to the number of occupied seats he or she will go through.
  
  Let's consider an example: m = 5, the person has the seat 4 in the first row, the seats 1, 3, 5 in the first row are already occupied, the seats 2 and 4 are free. The inconvenience of this person will be 2, because he will go through occupied seats 1 and 3.
  
  Find the minimal total inconvenience (the sum of inconveniences of all people), that is possible to have by giving places for all people (all conditions should be satisfied).
  
  Input
  
  The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Description of the test cases follows.
  
  The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 300) — the number of rows and places in each row respectively.
  
  The second line of each test case contains n ⋅ m integers a_1, a_2, …, a_{n ⋅ m} (1 ≤ a_i ≤ 10^9), where a_i is the sight level of i-th person.
  
  It's guaranteed that the sum of n ⋅ m over all test cases does not exceed 10^5.
  
  Output
  
  For each test case print a single integer — the minimal total inconvenience that can be achieved.
  
  Example
  
  Input
  
  
  7
  1 2
  1 2
  3 2
  1 1 2 2 3 3
  3 3
  3 4 4 1 1 1 1 1 2
  2 2
  1 1 2 1
  4 2
  50 50 50 50 3 50 50 50
  4 2
  6 6 6 6 2 2 9 6
  2 9
  1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3
  
  
  Output
  
  
  1
  0
  4
  0
  0
  0
  1
  
  Note
  
  In the first test case, there is a single way to give seats: the first person sits in the first place and the second person — in the second. The total inconvenience is 1.
  
  In the second test case the optimal seating looks like this: 
  
  <image>
  
  In the third test case the optimal seating looks like this: 
  
  <image>
  
  The number in a cell is the person's index that sits on this place.
solution: import java.io.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.OutputStream;
  import java.io.PrintStream;
  import java.util.Arrays;
  import java.io.IOException;
  import java.lang.reflect.Field;
  import java.nio.charset.StandardCharsets;
  import java.io.UncheckedIOException;
  import java.io.Closeable;
  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) throws Exception {
          Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
          thread.start();
          thread.join();
      }
  
      static class TaskAdapter implements Runnable {
          @Override
          public void run() {
              InputStream inputStream = System.in;
              OutputStream outputStream = System.out;
              FastInput in = new FastInput(inputStream);
              FastOutput out = new FastOutput(outputStream);
              D2SeatingArrangementsHardVersion solver = new D2SeatingArrangementsHardVersion();
              int testCount = Integer.parseInt(in.next());
              for (int i = 1; i <= testCount; i++)
                  solver.solve(i, in, out);
              out.close();
          }
      }
  
      static class D2SeatingArrangementsHardVersion {
          Debug debug = new Debug(false);
  
          public void solve(int testNumber, FastInput in, FastOutput out) {
              int n = in.ri();
              int m = in.ri();
              IntegerBIT[] rows = new IntegerBIT[n];
              for (int i = 0; i < n; i++) {
                  rows[i] = new IntegerBIT(m);
              }
              Person[] people = new Person[n * m];
              for (int i = 0; i < n * m; i++) {
                  people[i] = new Person();
                  people[i].a = in.ri();
                  people[i].order = i;
              }
              Person[] sorted = people.clone();
              Arrays.sort(sorted, Comparator.comparingInt(x -> x.a));
              int nm = n * m;
              for (int i = 0; i < nm; i++) {
                  int l = i;
                  int r = i;
                  while (r + 1 < nm && sorted[r + 1].a == sorted[i].a) {
                      r++;
                  }
                  i = r;
                  Person[] consider = Arrays.copyOfRange(sorted, l, r + 1);
                  int iter = 0;
                  for (int j = l; j <= r; j++) {
                      int L = j;
                      int R = j;
                      while (R + 1 <= r && (R + 1) / m == j / m) {
                          R++;
                      }
                      j = R;
                      for (int t = R; t >= L; t--) {
                          consider[iter++].assign = t;
                      }
                  }
              }
              boolean[] used = new boolean[nm];
              for (Person p : people) {
                  used[p.assign] = true;
              }
              for (int i = 0; i < nm; i++) {
                  assert used[i];
              }
              long cost = 0;
              for (Person p : people) {
                  int r = p.assign / m;
                  int c = p.assign % m;
                  cost += rows[r].query(c + 1);
                  rows[r].update(c + 1, 1);
              }
              out.println(cost);
              debug.debug("people", people);
          }
  
      }
  
      static class FastInput {
          private final InputStream is;
          private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
          private byte[] buf = new byte[1 << 13];
          private int bufLen;
          private int bufOffset;
          private int next;
  
          public FastInput(InputStream is) {
              this.is = is;
          }
  
          private int read() {
              while (bufLen == bufOffset) {
                  bufOffset = 0;
                  try {
                      bufLen = is.read(buf);
                  } catch (IOException e) {
                      bufLen = -1;
                  }
                  if (bufLen == -1) {
                      return -1;
                  }
              }
              return buf[bufOffset++];
          }
  
          public void skipBlank() {
              while (next >= 0 && next <= 32) {
                  next = read();
              }
          }
  
          public String next() {
              return readString();
          }
  
          public int ri() {
              return readInt();
          }
  
          public int readInt() {
              boolean rev = false;
  
              skipBlank();
              if (next == '+' || next == '-') {
                  rev = next == '-';
                  next = read();
              }
  
              int val = 0;
              while (next >= '0' && next <= '9') {
                  val = val * 10 - next + '0';
                  next = read();
              }
  
              return rev ? val : -val;
          }
  
          public String readString(StringBuilder builder) {
              skipBlank();
  
              while (next > 32) {
                  builder.append((char) next);
                  next = read();
              }
  
              return builder.toString();
          }
  
          public String readString() {
              defaultStringBuf.setLength(0);
              return readString(defaultStringBuf);
          }
  
      }
  
      static class Person {
          int order;
          int a;
          int assign;
  
          public String toString() {
              return "Person{" +
                      "order=" + order +
                      ", assign=" + assign +
                      '}';
          }
  
      }
  
      static class IntegerBIT {
          private int[] data;
          private int n;
  
          public IntegerBIT(int n) {
              this.n = n;
              data = new int[n + 1];
          }
  
          public int query(int i) {
              i = Math.min(i, n);
              int sum = 0;
              for (; i > 0; i -= i & -i) {
                  sum += data[i];
              }
              return sum;
          }
  
          public void update(int i, int mod) {
              if (i <= 0) {
                  return;
              }
              for (; i <= n; i += i & -i) {
                  data[i] += mod;
              }
          }
  
          public String toString() {
              StringBuilder builder = new StringBuilder();
              for (int i = 1; i <= n; i++) {
                  builder.append(query(i) - query(i - 1)).append(' ');
              }
              return builder.toString();
          }
  
      }
  
      static class Debug {
          private boolean offline;
          private PrintStream out = System.err;
          static int[] empty = new int[0];
  
          public Debug(boolean enable) {
              offline = enable && System.getSecurityManager() == null;
          }
  
          public Debug debug(String name, Object x) {
              return debug(name, x, empty);
          }
  
          public Debug debug(String name, Object x, int... indexes) {
              if (offline) {
                  if (x == null || !x.getClass().isArray()) {
                      out.append(name);
                      for (int i : indexes) {
                          out.printf("[%d]", i);
                      }
                      out.append("=").append("" + x);
                      out.println();
                  } else {
                      indexes = Arrays.copyOf(indexes, indexes.length + 1);
                      if (x instanceof byte[]) {
                          byte[] arr = (byte[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof short[]) {
                          short[] arr = (short[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof boolean[]) {
                          boolean[] arr = (boolean[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof char[]) {
                          char[] arr = (char[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof int[]) {
                          int[] arr = (int[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof float[]) {
                          float[] arr = (float[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof double[]) {
                          double[] arr = (double[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else if (x instanceof long[]) {
                          long[] arr = (long[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      } else {
                          Object[] arr = (Object[]) x;
                          for (int i = 0; i < arr.length; i++) {
                              indexes[indexes.length - 1] = i;
                              debug(name, arr[i], indexes);
                          }
                      }
                  }
              }
              return this;
          }
  
      }
  
      static class FastOutput implements AutoCloseable, Closeable, Appendable {
          private static final int THRESHOLD = 32 << 10;
          private OutputStream writer;
          private StringBuilder cache = new StringBuilder(THRESHOLD * 2);
          private static Field stringBuilderValueField;
          private char[] charBuf = new char[THRESHOLD * 2];
          private byte[] byteBuf = new byte[THRESHOLD * 2];
  
          static {
              try {
                  stringBuilderValueField = StringBuilder.class.getSuperclass().getDeclaredField("value");
                  stringBuilderValueField.setAccessible(true);
              } catch (Exception e) {
                  stringBuilderValueField = null;
              }
              stringBuilderValueField = null;
          }
  
          public FastOutput append(CharSequence csq) {
              cache.append(csq);
              return this;
          }
  
          public FastOutput append(CharSequence csq, int start, int end) {
              cache.append(csq, start, end);
              return this;
          }
  
          private void afterWrite() {
              if (cache.length() < THRESHOLD) {
                  return;
              }
              flush();
          }
  
          public FastOutput(OutputStream writer) {
              this.writer = writer;
          }
  
          public FastOutput append(char c) {
              cache.append(c);
              afterWrite();
              return this;
          }
  
          public FastOutput append(long c) {
              cache.append(c);
              afterWrite();
              return this;
          }
  
          public FastOutput println(long c) {
              return append(c).println();
          }
  
          public FastOutput println() {
              return append('\n');
          }
  
          public FastOutput flush() {
              try {
                  if (stringBuilderValueField != null) {
                      try {
                          byte[] value = (byte[]) stringBuilderValueField.get(cache);
                          writer.write(value, 0, cache.length());
                      } catch (Exception e) {
                          stringBuilderValueField = null;
                      }
                  }
                  if (stringBuilderValueField == null) {
                      int n = cache.length();
                      if (n > byteBuf.length) {
                          //slow
                          writer.write(cache.toString().getBytes(StandardCharsets.UTF_8));
  //                writer.append(cache);
                      } else {
                          cache.getChars(0, n, charBuf, 0);
                          for (int i = 0; i < n; i++) {
                              byteBuf[i] = (byte) charBuf[i];
                          }
                          writer.write(byteBuf, 0, n);
                      }
                  }
                  writer.flush();
                  cache.setLength(0);
              } catch (IOException e) {
                  throw new UncheckedIOException(e);
              }
              return this;
          }
  
          public void close() {
              flush();
              try {
                  writer.close();
              } catch (IOException e) {
                  throw new UncheckedIOException(e);
              }
          }
  
          public String toString() {
              return cache.toString();
          }
  
      }
  }
  
  