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.util.*;
  import java.io.*;
  
  public class Main {
  
      static long startTime = System.currentTimeMillis();
  
      // for global initializations and methods starts here
  
      static class FenwickTree {
          int[] a;
  
          FenwickTree(int n) {
              a = new int[n];
          }
  
          public void add(int pos, int val) {
              while (pos < a.length) {
                  a[pos] += val;
                  pos |= pos + 1;
              }
          }
  
          public int sum(int r) {
              int res = 0;
              while (r >= 0) {
                  res += a[r];
                  r = (r & (r + 1)) - 1;
              }
              return res;
          }
      }
  
      // 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) {
  
                  int n = r.ni();
                  int m = r.ni();
  
                  List<Integer> a = new ArrayList<>();
                  for (int i = 0; i < n * m; i++) a.add(r.ni());
  
                  List<Integer> temp = new ArrayList<>();
                  for (int i = 0; i < a.size(); i++) temp.add(i);
  
                  temp.sort((x, y) -> {
                      if (!Objects.equals(a.get(x), a.get(y))) {
                          return a.get(x) < a.get(y) ? -1 : 1;
                      }
                      if (!x.equals(y)) {
                          return x < y ? -1 : 1;
                      }
                      return 0;
                  });
  
                  int[] row = new int[temp.size()];
                  int[] col = new int[temp.size()];
                  long ans = 0;
  
                  for (int j = 0; j < n; j++) {
                      List<Integer> p = new ArrayList<>();
                      for (int i = j * m; i < (j + 1) * m; i++) p.add(temp.get(i));
                      p.sort((x, y) -> {
                          if (!Objects.equals(a.get(x), a.get(y))) {
                              return a.get(x) < a.get(y) ? -1 : 1;
                          }
                          if (!x.equals(y)) {
                              return x > y ? -1 : 1;
                          }
                          return 0;
                      });
  
                      for (int i = 0; i < p.size(); i++) {
                          row[p.get(i)] = j;
                          col[p.get(i)] = i;
                      }
                  }
  
                  FenwickTree[] fwt = new FenwickTree[n];
                  for (int i = 0; i < n; i++) {
                      fwt[i] = new FenwickTree(m);
                  }
  
                  for (int i = 0; i < a.size(); i++) {
                      FenwickTree t = fwt[row[i]];
                      ans += t.sum(col[i]);
                      t.add(col[i], 1);
                  }
  
                  out.write((ans + " ").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> {
          int first;
          int second;
  
          public Pair(int first, int 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;
      }
  
  }