description: There are n points and m segments on the coordinate line. The initial coordinate of the i-th point is a_i. The endpoints of the j-th segment are l_j and r_j — left and right endpoints, respectively.
  
  You can move the points. In one move you can move any point from its current coordinate x to the coordinate x - 1 or the coordinate x + 1. The cost of this move is 1.
  
  You should move the points in such a way that each segment is visited by at least one point. A point visits the segment [l, r] if there is a moment when its coordinate was on the segment [l, r] (including endpoints).
  
  You should find the minimal possible total cost of all moves such that all segments are visited.
  
  Input
  
  The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — 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 ≤ 2 ⋅ 10^5) — the number of points and segments respectively.
  
  The next line contains n distinct integers a_1, a_2, …, a_n (-10^9 ≤ a_i ≤ 10^9) — the initial coordinates of the points.
  
  Each of the next m lines contains two integers l_j, r_j (-10^9 ≤ l_j ≤ r_j ≤ 10^9) — the left and the right endpoints of the j-th segment.
  
  It's guaranteed that the sum of n and the sum of m over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  For each test case print a single integer — the minimal total cost of all moves such that all segments are visited.
  
  Example
  
  Input
  
  
  2
  4 11
  2 6 14 18
  0 3
  4 5
  11 15
  3 5
  10 13
  16 16
  1 4
  8 12
  17 19
  7 13
  14 19
  4 12
  -9 -16 12 3
  -20 -18
  -14 -13
  -10 -7
  -3 -1
  0 4
  6 11
  7 9
  8 10
  13 15
  14 18
  16 17
  18 19
  
  
  Output
  
  
  5
  22
  
  Note
  
  In the first test case the points can be moved as follows:
  
    * Move the second point from the coordinate 6 to the coordinate 5. 
    * Move the third point from the coordinate 14 to the coordinate 13. 
    * Move the fourth point from the coordinate 18 to the coordinate 17. 
    * Move the third point from the coordinate 13 to the coordinate 12. 
    * Move the fourth point from the coordinate 17 to the coordinate 16. 
  
  
  
  The total cost of moves is 5. It is easy to see, that all segments are visited by these movements. For example, the tenth segment ([7, 13]) is visited after the second move by the third point.
  
  Here is the image that describes the first test case:
  
  <image>
solution: //package lamphanviet.onlinejudges.codeforces.globalround16;
  
  import java.io.*;
  import java.util.*;
  
  public class Main {
      static final boolean FROM_FILE = false;
  
      static class Solution {
          int n, m;
          int[] points;
          TreeSet<Integer> sortedPoints;
          List<Line> lines;
          List<Item> items;
  
          void solve(final int caseNumber) {
              n = in.nextInt();
              m = in.nextInt();
              points = new int[n];
              sortedPoints = new TreeSet<>();
              for (int i = 0; i < n; i++) {
                  points[i] = in.nextInt();
                  sortedPoints.add(points[i]);
              }
  
              lines = new ArrayList<>();
              for (int i = 0; i < m; i++) {
                  Line line = new Line();
                  line.x = in.nextInt();
                  line.y = in.nextInt();
                  if (!overlapWithAnyPoint(line)) {
                      lines.add(line);
                  }
              }
  
  //            out.printf("m %d -> %d\n", m, lines.size());
              m = lines.size();
              for (int i = 0; i < m; i++) {
                  lines.get(i).index = i;
              }
  
              items = new ArrayList<>();
              for (int i = 0; i < n; i++) {
                  Item item = new Item();
                  item.isPoint = true;
                  item.x = points[i];
                  items.add(item);
              }
              for (Line line : lines) {
                  Item item = new Item();
                  item.isLineStart = true;
                  item.x = line.x;
                  item.lineIndex = line.index;
                  items.add(item);
  
                  item = new Item();
                  item.isLineStart = false;
                  item.x = line.y;
                  item.lineIndex = line.index;
                  items.add(item);
              }
  
              items.sort((a, b) -> {
                  if (a.x == b.x) {
                      if (a.isPoint && b.isPoint) {
                          return 0;
                      }
                      if (a.isPoint) return -1;
                      if (b.isPoint) return 1;
                      return a.lineIndex - b.lineIndex;
                  }
                  return a.x - b.x;
              });
  
  //            out.printf("Case %d\n", caseNumber);
              out.println(dp());
          }
  
          long dp() {
              if (lines.size() == 0) {
                  return 0;
              }
              final int k = items.size();
              long[] fGone = new long[k];
              long[] fBack = new long[k];
              int lastPointIndex = -1;
              int lastStartIndex = -1;
              for (int i = 0; i < k; i++) {
                  Item cur = items.get(i);
                  if (cur.isLineStart) lastStartIndex = i;
  
                  if (!cur.isPoint) {
                      continue;
                  }
  
                  if (lastPointIndex < 0) {
                      int firstEndIndex = 0;
                      for (int j = 0; j < i; j++) {
                          if (!items.get(j).isLineStart) {
                              firstEndIndex = j;
                              break;
                          }
                      }
                      fGone[i] = getDistance(firstEndIndex, i);
                      fBack[i] = fGone[i] * 2; // must go back.
                  } else {
                      TreeSet<Line> inLines = new TreeSet<>((a, b) -> {
                          if (a.x == b.x) {
                              return a.index - b.index;
                          }
                          return a.x - b.x;
                      });
                      for (int j = lastPointIndex + 1; j < i; j++) {
                          if (items.get(j).isLineStart) inLines.add(lines.get(items.get(j).lineIndex));
                      }
  
                      if (inLines.size() == 0) {
                          // no lines in between.
                          fBack[i] = fGone[i] = fGone[lastPointIndex];
                      } else {
                          // stay there
                          long d = inLines.last().x - items.get(lastPointIndex).x;
                          fBack[i] = fGone[i] = Math.min(fBack[lastPointIndex] + d, fGone[lastPointIndex] + d * 2);
                      }
  
                      // lastPointIndex ----> lastStart ---> firstEnd -----> i.
                      for (int j = i - 1; j > lastPointIndex; j--) {
                          if (!items.get(j).isLineStart) {
                              // removing all lines covered at this position
                              int jj = j;
                              while (jj > lastPointIndex && items.get(jj).x == items.get(j).x) {
                                  inLines.remove(lines.get(items.get(jj).lineIndex));
                                  jj--;
                              }
                              long firstHalf = 0;
                              if (inLines.size() > 0) {
                                  long d = (inLines.last().x - items.get(lastPointIndex).x);
                                  firstHalf = Math.min(fBack[lastPointIndex] + d, fGone[lastPointIndex] + d * 2);
                              } else {
                                  firstHalf = fGone[lastPointIndex];
                              }
  
                              long secondHalf = getDistance(j, i);
                              fGone[i] = Math.min(fGone[i], firstHalf + secondHalf);
                              fBack[i] = Math.min(fBack[i], firstHalf + secondHalf * 2);
  
                              j = jj + 1;
                          }
                      }
                  }
                  lastPointIndex = i;
              }
  
  //            for (int i = 0; i < k; i++) {
  //                out.printf("%s  :  gone %d back %d\n", items.get(i), fGone[i], fBack[i]);
  //            }
  //            out.println();
  
  //            for (int i = 0; i < k; i++) {
  //                if (fBack[i] < fGone[i]) {
  //                    throw new RuntimeException("not possible.");
  //                }
  //            }
  
              if (lastPointIndex == k - 1) {
                  return Math.min(fGone[lastPointIndex], fBack[lastPointIndex]);
              }
  
              // cover the lines in [lastPointIndex + 1 -> k - 1].
              long d = getDistance(lastPointIndex, lastStartIndex);
              return Math.min(fBack[lastPointIndex] + d, fGone[lastPointIndex] + d * 2);
          }
  
          int getDistance(int i, int j) {
              if (i < 0 || j < 0 || i >= items.size() || j >= items.size()) {
                  return 0;
              }
              return items.get(j).x - items.get(i).x;
          }
  
          boolean overlapWithAnyPoint(Line line) {
              Integer lower = sortedPoints.lower(line.y + 1);
              if (lower == null) {
                  return false;
              }
              return line.x <= lower;
          }
      }
  
      static class State {
          long best;
      }
  
      static class Item {
          boolean isPoint;
          boolean isLineStart;
          int x;
          int lineIndex;
  
          public String toString() {
              if (isPoint) return String.format("(point: %d)", x);
              return String.format("(line %s: %d, index %d)", isLineStart ? "start" : "end", x, lineIndex);
          }
      }
  
      static class Line {
          int x, y;
          int index;
          Line() {}
          Line(int x, int y) {
              this.x = x;
              this.y = y;
          }
          Line(int x, int y, int index) {
              this.x = x;
              this.y = y;
              this.index = index;
          }
      }
  
      /************
       * TEMPLATE *
       ************/
      static void runTestCase(final int caseNumber) {
          (new Solution()).solve(caseNumber);
      }
  
      public static void main(final String[] args) {
          final int cases = in.nextInt();
          // final int cases = 1;
          for (int caseNumber = 1; caseNumber <= cases; caseNumber++) {
              runTestCase(caseNumber);
          }
          out.close();
      }
  
      static final String PATH = "tst/";
      static final String INPUT_FILE = "input.txt";
      static final String OUTPUT_FILE = "output.txt";
      static final FastReader in;
      static final PrintWriter out;
  
      static {
          try {
              if (FROM_FILE) {
                  in = new FastReader(new FileReader(PATH + INPUT_FILE));
                  out = new PrintWriter(new FileWriter(PATH + OUTPUT_FILE));
              } else {
                  in = new FastReader();
                  out = new PrintWriter(new OutputStreamWriter(System.out));
              }
          } catch (final Exception e) {
              throw new RuntimeException("I/O issue.", e);
          }
      }
  
      static class FastReader {
          private final BufferedReader bufferedReader;
          private StringTokenizer stringTokenizer;
  
          public FastReader() {
              bufferedReader = new BufferedReader(new InputStreamReader(System.in));
          }
  
          public FastReader(final InputStreamReader inputStreamReader) {
              bufferedReader = new BufferedReader(inputStreamReader);
          }
  
          public String next() {
              while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                  try {
                      stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                  } catch (final Throwable e) {
                      e.printStackTrace();
                  }
              }
              return stringTokenizer.nextToken();
          }
  
          public int nextInt() {
              return Integer.parseInt(next());
          }
  
          public long nextLong() {
              return Long.parseLong(next());
          }
  
          public double nextDouble() {
              return Double.parseDouble(next());
          }
  
          public String nextLine() {
              try {
                  return bufferedReader.readLine();
              } catch (IOException e) {
                  e.printStackTrace();
              }
              return "";
          }
      }
  }