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.sql.SQLSyntaxErrorException;
  import java.util.*;
  import java.io.*;
  import java.util.stream.StreamSupport;
  
  
  public class Solution {
      static int mod = 998244353;
      public static void main(String str[]) throws IOException{
  //        Reader sc = new Reader();
          BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
          Scanner sc = new Scanner(System.in);
          int t = sc.nextInt();
          sc.nextLine();
          while(t-->0){
              int n = sc.nextInt();
              int m = sc.nextInt();
              Pair[] arr = new Pair[n*m];
              for(int i=0;i<n*m;i++){
                  int x = sc.nextInt();
                  arr[i] = new Pair(i,x);
              }
              Arrays.sort(arr, new Comparator<Pair>() {
                  @Override
                  public int compare( Pair p1, Pair p2) {
                          if(p1.value>p2.value)   return 1;
                          else if(p1.value==p2.value){
                              if(p1.ind<p2.ind){
                                  return 1;
                              }
                              else    return -1;
                          }
                          else    return -1;
                      }
              });
              ArrayList<ArrayList<Pair>> store = new ArrayList<>();
              for(int i=0;i<n;i++){
                  ArrayList<Pair> temp = new ArrayList<>();
                  for(int j=0;j<m;j++){
                      Pair p = new Pair(arr[i*m + j].ind, arr[i*m + j].value);
                      temp.add(p);
                  }
                  store.add(temp);
              }
  
              int val = -1;
              int ind = 0;
              int jind = 0;
  
  
              for(int i=0;i<n;i++){
                  for(int j=0;j<m;j++){
                      int v = store.get(i).get(j).value;
  
                      if(val!=-1 && ( (i==(n-1) && j==(m-1) || (j<m-1 && store.get(i).get(j+1).value!=v) || (j==m-1 && store.get(i+1).get(0).value!=v)))){
                          if(i>ind){
                              int min = Math.min(m-jind, j+1);
                              int l = m-1;
                              int s = 0;
                              for(int x=0;x<min;x++){
                                  Pair p1 = store.get(ind).get(jind);
                                  Pair p2 = store.get(i).get(j);
                                  store.get(ind).remove(jind);
                                  store.get(i).remove(j);
                                  store.get(i).add(s,p1);
                                  store.get(ind).add(l,p2);
                                  s++;
                                  l--;
                              }
                              if(i-ind>1){
                                  if(s<=j){
                                      ind++;
                                      jind = 0;
                                      l = m-1;
                                      while(s<=j){
                                          Pair p1 = store.get(ind).get(jind);
                                          Pair p2 = store.get(i).get(j);
                                          store.get(ind).remove(jind);
                                          store.get(i).remove(j);
                                          store.get(i).add(s,p1);
                                          store.get(ind).add(l,p2);
                                          s++;
                                          l--;
                                      }
                                  }
                                  else if(l>=jind){
                                      int ii = i-1;
                                      int jj = m-1;
                                      s = 0;
                                      while(l>=jind){
                                          Pair p1 = store.get(ind).get(jind);
                                          Pair p2 = store.get(ii).get(jj);
                                          store.get(ind).remove(jind);
                                          store.get(ii).remove(jj);
                                          store.get(ii).add(s,p1);
                                          store.get(ind).add(l,p2);
                                          s++;
                                          l--;
                                      }
                                  }
                              }
                          }
                          val = -1;
                      }
                      else{
                          if(val==-1 && ( (j<m-1 && store.get(i).get(j+1).value==v) || (i<n-1 && j==m-1 && store.get(i+1).get(0).value==v))) {
                              val = store.get(i).get(j).value;
                              ind = i;
                              jind = j;
                          }
                      }
                  }
              }
              int ans = 0;
              for(int i=0;i<n;i++) {
                  ArrayList<Integer> al = new ArrayList<>();
                  for (int j = 0; j < m; j++) {
                      int x = Collections.binarySearch(al, store.get(i).get(j).ind);
                      if (x < 0) x = (x * -1) - 1;
                      ans += x;
                      al.add(x, store.get(i).get(j).ind);
                  }
              }
              System.out.println(ans);
          }
  
          output.flush();
      }
  
  
  
      static class Pair {
          int ind;
          int value;
          Pair(int i, int v) {
              ind = i;
              value = v;
          }
      }
      static class Node{
          int ind;
          long total = -1;
          int dis = 0;
          Map<Integer, Long> map = new HashMap<>();
          ArrayList<Pair> al = new ArrayList<>();
          Node(int i){
              ind =i;
          }
      }
      static int maxHeight(List<Integer> wallPositions, List<Integer> wallHeights){
          int ans = 0;
          int n = wallHeights.size();
          for(int i=1;i<n;i++){
              int ind1 = wallPositions.get(i-1);
              int ind2 = wallPositions.get(i);
              if(ind2-ind1==1)    continue;
              int x = wallHeights.get(i-1);
              int y = wallHeights.get(i);
              int index = (y-x+ind1+ind2)/2;
              if(index<=ind1){
                  index = ind1+1;
              }
              else if(index>=ind2){
                  index = ind2-1;
              }
              ans = Math.max(ans, Math.min(x+(index-ind1),y+(ind2-index)));
          }
          return ans;
      }
  
  
  
  
  //        3
  //        2 1 1
  //        2 3 1
  //        3 4 1
  //        4
  //        2
  
  
      public static ArrayList<Integer> primeFactors(int n)
      {
          // Print the number of 2s that divide n
          ArrayList<Integer> al = new ArrayList<>();
          while (n%2==0)
          {
              al.add(2);
              n /= 2;
          }
  
          // n must be odd at this point.  So we can
          // skip one element (Note i = i +2)
          for (int i = 3; i <= Math.sqrt(n); i+= 2)
          {
              // While i divides n, print i and divide n
              while (n%i == 0)
              {
                  al.add(i);
                  n /= i;
              }
          }
  
          // This condition is to handle the case whien
          // n is a prime number greater than 2
          if (n > 2)
              al.add(n);
  
          return al;
      }
  
  
  
  
      static void bfs(Graph[] g, int ind, boolean vis[], ArrayList<Node> al, Set<Integer> set){
          vis[ind] = true;
          set.add(ind);
          for(int i: g[ind].pq){
              if(!vis[i])     bfs(g,i,vis,al,set);
          }
          g[ind].set = set;
      }
  
  
  //    static class tempSort implements Comparator<Node> {
  //        // Used for sorting in ascending order of
  //        // roll number
  //        public int compare(Node a, Node b) {
  //            return a.size - b.size;
  //        }
  //    }
  
  
  
  
  
      static long divide(long p, long q, long mod)
      {
          long expo = mod - 2;
  
          while (expo != 0)
          {
              if ((expo & 1) == 1)
              {
  //                long temp = p;
  //                System.out.println("zero--> "+temp+" "+q);
                  p = (p * q) % mod;
  //                if(p<0){
  //                    System.out.println("one--> "+temp+" "+q);
  //                }
              }
              q = (q * q) % mod;
  //            if(q<0){
  //                System.out.println("two--> "+p+" "+q);
  //            }
  
              expo >>= 1;
          }
          return p;
      }
  
  
      static class Graph{
          int ind;
          ArrayList<Integer> pq = new ArrayList<>();
          Set<Integer> set;
          boolean b = false;
          public Graph(int a){
              ind = a;
          }
  
  
      }
  
  
      //
  //    static class Pair{
  //        int a=0;
  //        int b=0;
  //        int in = 0;
  //        int ac = 0;
  //        int ex = 0;
  //    }
      long fun2(ArrayList<Integer> arr, int x){
          ArrayList<ArrayList> al = new ArrayList<>();
          ArrayList<Integer> curr = new ArrayList<>();
          fun(arr, x, al, curr, 0);
          if(al.size()==0)    return 0;
          int max = 0;
          for(ArrayList<Integer> i: al){
              if(i.size()>max)    max = i.size();
          }
          for(int i=0;i<al.size();i++){
              if(al.get(i).size()!=max){
                  al.remove(i);
                  i--;
              }
          }
          for(ArrayList<Integer> i: al){
              Collections.sort(al, Collections.reverseOrder());
          }
          long ans = 0;
  
          for(ArrayList<Integer> i: al){
              long temp = 0;
              for(int j: i){
                  temp*=10;
                  temp+=j;
              }
              if(ans<temp)    ans = temp;
          }
          return ans;
  
      }
      void fun(ArrayList<Integer> arr, int x, ArrayList<ArrayList> al, ArrayList<Integer> curr, int i){
          if(x<0) return ;
          if(x==0) {
              al.add(curr);
              return;
          }
          for(int j=i;j<arr.size();j++){
              ArrayList<Integer> temp = new ArrayList<>(curr);
              fun(arr, x-arr.get(j), al, temp, j);
          }
      }
  
  
  
      // Returns n^(-1) mod p
      static long modInverse(long n, long p)
      {
          return (long)power(n, p - 2, p);
      }
  
  
  
      // Returns nCr % p using Fermat's
      // little theorem.
      static long nCrModPFermat(int n, int r,
                                int p, long[] fac)
      {
  
          if (n<r)
              return 0;
          // Base case
          if (r == 0)
              return 1;
  
          // Fill factorial array so that we
          // can find all factorial of r, n
          // and n-r
          long x = modInverse(fac[r], p);
          long y = modInverse(fac[n - r], p);
  
          return (fac[n] * x
                  % p * y
                  % p)
                  % p;
      }
  
      static long[] sum(String[] str){
          int n = str[0].length();
          long ans[] = new long[n];
          for(String s: str){
              for(int i=0;i<n;i++)   ans[i]+=s.charAt(i);
          }
          return ans;
      }
  
  //    static class tSort implements Comparator<Pair>{
  //
  //        public int compare(Pair s1, Pair s2) {
  //            if (s1.b < s2.b)
  //                return -1;
  //            else if (s1.b > s2.b)
  //                return 1;
  //            return 0;
  //        }
  //    }
  
  
  //    static boolean checkCycle(Tree[] arr,  boolean[] visited, int curr, int node){
  //        if(curr==node && visited[curr]) return true;
  //        if(visited[curr])   return false;
  //        visited[curr]  = true;
  //        for(int i: arr[curr].al){
  //            if(checkCycle(arr, visited, i, node))    return true;
  //        }
  //        return false;
  //    }
  
  
  //    static boolean allCombinations(int n){      //Global round 15
  //        int three2n = 1;
  //        for (int i = 1; i <= n; i++)
  //            three2n *= 3;
  //
  //        for (int k = 1; k < three2n; k++) {
  //            int k_cp = k;
  //            int sum = 0;
  //            for (int i = 1; i <= n; i++) {
  //                int s = k_cp % 3;
  //                k_cp /= 3;
  //                if (s == 2) s = -1;
  //                sum += s * a[i];
  //            }
  //            if (sum == 0) {
  //                return true;
  //            }
  //        }
  //        return false;
  //    }
  
      static ArrayList<String> fun( int curr, int n, char c){
          int len = n-curr;
          if(len==0)  return null;
          ArrayList<String> al = new ArrayList<>();
          if(len==1){
              al.add(c+"");
              return al;
          }
          String ss = "";
          for(int i=0;i<len/2;i++){
              ss+=c;
          }
          ArrayList<String> one = fun(len/2+curr, n, (char)(c+1));
          for(String str: one){
              al.add(str+ss);
              al.add(ss+str);
          }
          return al;
      }
      static ArrayList convert(int x, int k){
          ArrayList<Integer> al = new ArrayList<>();
          if(x>0) {
              while (x > 0) {
                  al.add(x % k);
                  x /= k;
              }
          }
          else    al.add(0);
          return al;
      }
  
  
  
  
      static int max(int x, int y, int z){
          int ans = Math.max(x,y);
          ans = Math.max(ans, z);
          return ans;
      }
      static int min(int x, int y, int z){
          int ans = Math.min(x,y);
          ans = Math.min(ans, z);
          return ans;
      }
  
  //    static long treeTraversal(Tree arr[], int parent, int x){
  //        long tot = 0;
  //        for(int i: arr[x].al){
  //            if(i!=parent){
  //                tot+=treeTraversal(arr, x, i);
  //            }
  //        }
  //        arr[x].child = tot;
  //        if(arr[x].child==0) arr[x].child = 1;
  //        return tot+1;
  //    }
  
      public static int primeFactors(int n, int k)
      {
          int ans = 0;
  
          while (n%2==0)
          {
              ans++;
              if(ans>=k)  return k;
              n /= 2;
          }
          for (int i = 3; i <= Math.sqrt(n); i+= 2)
          {
              while (n%i == 0)
              {
                  ans++;
                  n /= i;
                  if(ans>=k)  return k;
              }
          }
  
          if (n > 2)  ans++;
          return ans;
      }
      static int binaryLow(ArrayList<Integer> arr, int x, int s, int e){
          if(s>=e){
              if(arr.get(s)>=x)  return s;
              else    return s+1;
          }
          int m = (s+e)/2;
          if(arr.get(m)==x)  return m;
          if(arr.get(m)>x)   return binaryLow(arr,x,s,m);
          if(arr.get(m)<x)   return binaryLow(arr,x,m+1,e);
          return 0;
      }
      static int binaryLow(int[] arr, int x, int s, int e){
          if(s>=e){
              if(arr[s]>=x)  return s;
              else    return s+1;
          }
          int m = (s+e)/2;
          if(arr[m]==x)  return m;
          if(arr[m]>x)   return binaryLow(arr,x,s,m);
          if(arr[m]<x)   return binaryLow(arr,x,m+1,e);
          return 0;
      }
      static int binaryHigh(int[] arr, int x, int s, int e){
          if(s>=e){
              if(arr[s]<=x)  return s;
              else    return s-1;
          }
          int m = (s+e)/2;
          if(arr[m]==x)  return m;
          if(arr[m]>x)   return binaryHigh(arr,x,s,m-1);
          if(arr[m]<x)   return binaryHigh(arr,x,m+1,e);
          return 0;
      }
  
  
  //    static void arri(int arr[], int n, Reader sc) throws IOException{
  //        for(int i=0;i<n;i++){
  //            arr[i] = sc.nextInt();
  //        }
  //    }
  //    static void arrl(long arr[], int n, Reader sc) throws IOException{
  //        for(int i=0;i<n;i++){
  //            arr[i] = sc.nextLong();
  //        }
  
  
      static long gcd(long a, long b)
      {
          if (b == 0)
              return a;
          return gcd(b, a % b);
      }
      static long power(long x, long y, long p)
      {
          long res = 1; // Initialize result
  
          x = x % p; // Update x if it is more than or
          // equal to p
  
          if (x == 0)
              return 0; // In case x is divisible by p;
  
          while (y > 0)
          {
  
              // If y is odd, multiply x with result
              if ((y & 1) != 0)
                  res = (res * x) % p;
  
              // y must be even now
              y = y >> 1; // y = y/2
              x = (x * x) % p;
          }
          return res%p;
      }
  
  //    static boolean dfs(Tree node, boolean[] visited, int parent, ArrayList<Tree> tt){
  //        visited[node.a] = true;
  //        boolean b = false;
  //        for(int i: node.al){
  //            if(tt.get(i).a!=parent){
  //                if(visited[tt.get(i).a])    return true;
  //                b|= dfs(tt.get(i), visited, node.a, tt);
  //            }
  //        }
  //        return b;
  //    }
  
  
  
  
  //    static class SortbyI implements Comparator<Pair> {
  //        // Used for sorting in ascending order of
  //        // roll number
  //        public int compare(Pair a, Pair b)
  //        {
  //            if(a.a>=b.a) return 1;
  //            else return -1;
  //        }
  //    }
  //    static class SortbyD implements Comparator<Pair> {
  //        // Used for sorting in ascending order of
  //        // roll number
  //        public int compare(Pair a, Pair b)
  //        {
  //            if(a.a<b.a) return 1;
  //            else if(a.a==b.b && a.b>b.b)    return 1;
  //            else return -1;
  //        }
  //    }
  //    static int binarySearch(ArrayList<Pair> a, int x, int s, int e){
  //        if(s>=e){
  //            if(x<=a.get(s).b)  return s;
  //            else    return s+1;
  //        }
  //        int mid = (e+s)/2;
  //        if(a.get(mid).b<x){
  //            return binarySearch(a, x, mid+1, e);
  //        }
  //        else    return binarySearch(a,x,s, mid);
  //    }
  
      //    static class Edge{
  //        int a;
  //        int b;
  //        int c;
  //        int sec;
  //        Edge(int a, int b, int c, int sec){
  //            this.a = a;
  //            this.b = b;
  //            this.c = c;
  //            this.sec = sec;
  //        }
  //
  //    }
      static class Tree{
          int a;
  
          ArrayList<Tree> al = new ArrayList<>();
          Tree(int a){
              this.a = a;
          }
  
  
      }
  
      static class Reader {
          final private int BUFFER_SIZE = 1 << 16;
          private DataInputStream din;
          private byte[] buffer;
          private int bufferPointer, bytesRead;
  
          public Reader()
          {
              din = new DataInputStream(System.in);
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public Reader(String file_name) throws IOException
          {
              din = new DataInputStream(
                      new FileInputStream(file_name));
              buffer = new byte[BUFFER_SIZE];
              bufferPointer = bytesRead = 0;
          }
  
          public String readLine() throws IOException
          {
              byte[] buf = new byte[64]; // line length
              int cnt = 0, c;
              while ((c = read()) != -1) {
                  if (c == '\n') {
                      if (cnt != 0) {
                          break;
                      }
                      else {
                          continue;
                      }
                  }
                  buf[cnt++] = (byte)c;
              }
              return new String(buf, 0, cnt);
          }
  
          public int nextInt() 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 nextLong() 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 nextDouble() 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();
          }
      }
  
  
      static boolean isPrime(int n)
      {
          if (n <= 1)
              return false;
          if (n <= 3)
              return true;
          if (n % 2 == 0 ||
                  n % 3 == 0)
              return false;
  
          for (int i = 5;
               i * i <= n; i = i + 6)
              if (n % i == 0 ||
                      n % (i + 2) == 0)
                  return false;
  
          return true;
      }
      static ArrayList<Integer> sieveOfEratosthenes(int n)
      {
          ArrayList<Integer> al = new ArrayList<>();
          // Create a boolean array
          // "prime[0..n]" and
          // initialize all entries
          // it as true. A value in
          // prime[i] will finally be
          // false if i is Not a
          // prime, else true.
          boolean prime[] = new boolean[n + 1];
          for (int i = 0; i <= n; i++)
              prime[i] = true;
  
          for (int p = 2; p * p <= n; p++)
          {
              // If prime[p] is not changed, then it is a
              // prime
              if (prime[p] == true)
              {
                  // Update all multiples of p
                  for (int i = p * p; i <= n; i += p)
                      prime[i] = false;
              }
          }
  
          // Print all prime numbers
          for (int i = 2; i <= n; i++)
          {
              if (prime[i] == true)
                  al.add(i);
          }
          return al;
      }
  
  }