Problem:
Score : 300 points

Problem Statement

Dolphin resides in two-dimensional Cartesian plane, with the positive x-axis pointing right and the positive y-axis pointing up.

Currently, he is located at the point (sx,sy). In each second, he can move up, down, left or right by a distance of 1.

Here, both the x- and y-coordinates before and after each movement must be integers.

He will first visit the point (tx,ty) where sx < tx and sy < ty, then go back to the point (sx,sy), then visit the point (tx,ty) again, and lastly go back to the point (sx,sy).

Here, during the whole travel, he is not allowed to pass through the same point more than once, except the points (sx,sy) and (tx,ty).

Under this condition, find a shortest path for him.

Constraints

-1000 ≤ sx < tx ≤ 1000

-1000 ≤ sy < ty ≤ 1000

sx,sy,tx and ty are integers.

Input

The input is given from Standard Input in the following format:

sx sy tx ty

Output

Print a string S that represents a shortest path for Dolphin.

The i-th character in S should correspond to his i-th movement.

The directions of the movements should be indicated by the following characters:

U: Up

D: Down

L: Left

R: Right

If there exist multiple shortest paths under the condition, print any of them.

Sample Input 1

0 0 1 2

Sample Output 1

UURDDLLUUURRDRDDDLLU

One possible shortest path is:

Going from (sx,sy) to (tx,ty) for the first time: (0,0) → (0,1) → (0,2) → (1,2)

Going from (tx,ty) to (sx,sy) for the first time: (1,2) → (1,1) → (1,0) → (0,0)

Going from (sx,sy) to (tx,ty) for the second time: (0,0) → (-1,0) → (-1,1) → (-1,2) → (-1,3) → (0,3) → (1,3) → (1,2)

Going from (tx,ty) to (sx,sy) for the second time: (1,2) → (2,2) → (2,1) → (2,0) → (2,-1) → (1,-1) → (0,-1) → (0,0)

Sample Input 2

-2 -2 1 1

Sample Output 2

UURRURRDDDLLDLLULUUURRURRDDDLLDL

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

class hawawa
{
  static Printer sw = new Printer(Console.OpenStandardOutput()) { AutoFlush = false };

  static void Main()
  {
    Console.SetOut(sw);
    solve();
    Console.Out.Flush();
  }

  static int sx, sy, tx, ty;
  static Set<Tuple<int, int> > set = new Set<Tuple<int, int>>();

  static void solve()
  {
    Scanner scanner = new Scanner();
    sx = scanner.nextInt();
    sy = scanner.nextInt();
    tx = scanner.nextInt();
    ty = scanner.nextInt();
    Queue<Tuple<int, int, string>> queue = new Queue<Tuple<int, int, string>>();
    int cnt = 0;
    queue.Enqueue(Tuple.Create(0, 0, ""));
    while(queue.Count != 0)
    {
      var status = queue.Dequeue();
      int x = status.Item1, y = status.Item2;
      if (set.Contains(Tuple.Create(status.Item1, status.Item2))) continue;
      string str = status.Item3;
      if (x == tx && y == ty)
      {
        Console.Write(str);
        int xx = sx, yy = sy;
        foreach(var s in str)
        {
          switch (s)
          {
            case 'U':
              yy++;
              break;
            case 'D':
              yy--;
              break;
            case 'R':
              xx++;
              break;
            case 'L':
              xx--;
              break;
          }
          if ((xx == sx && yy == sy) || (xx == tx && yy == ty)) continue;
          set.Insert(Tuple.Create(xx, yy));
        }
        cnt++;
        if(cnt == 4)
        {
          Console.WriteLine();
          return;
        }
        int tmp = tx;
        tx = sx;
        sx = tmp;
        tmp = ty;
        ty = sy;
        sy = tmp;
      }
      for(int i = 0; i < 4; i++)
      {
        queue.Enqueue(Tuple.Create(x + dx[i], y + dy[i], str + d[i]));
      }
    }
  }
  static string[] d = new string[]{"U", "R", "D", "L"};
  static int[] dx = { 0, 1, 0, -1 };
  static int[] dy = { 1, 0, -1, 0 };

  static int comp(KeyValuePair<string, int> x, KeyValuePair<string, int> y)
  {
    if (x.Value < y.Value || (x.Value == y.Value && string.Compare(x.Key, y.Key) > 0)) return 1;
    if (x.Value > y.Value || (x.Value == y.Value && string.Compare(x.Key, y.Key) < 0)) return -1;
    return 0;
  }
}

class Scanner
{
  string[] s;
  int i;


  char[] cs = new char[] { ' ' };

  public Scanner()
  {
    s = new string[0];
    i = 0;
  }

  public string next()
  {
    if (i < s.Length) return s[i++];
    string st = Console.ReadLine();
    while (st == "") st = Console.ReadLine();
    s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
    i = 0;
    return next();
  }

  public int nextInt()
  {
    return int.Parse(next());
  }

  public long nextLong()
  {
    return long.Parse(next());
  }

  public double nextDouble()
  {
    return double.Parse(next());
  }

}

class Printer : StreamWriter
{
  public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
  public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
  public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { }
}

/// <summary>
/// Self-Balancing Binary Search Tree
/// (using Randamized BST)
/// </summary>
public class SB_BinarySearchTree<T> where T : IComparable
{
  public class Node
  {
    public T Value;
    public Node LChild;
    public Node RChild;
    public int Count;     //size of the sub tree

    public Node(T v)
    {
      Value = v;
      Count = 1;
    }
  }

  static Random _rnd = new Random();

  public static int Count(Node t)
  {
    return t == null ? 0 : t.Count;
  }

  static Node Update(Node t)
  {
    t.Count = Count(t.LChild) + Count(t.RChild) + 1;
    return t;
  }

  public static Node Merge(Node l, Node r)
  {
    if (l == null || r == null) return l == null ? r : l;

    if ((double)Count(l) / (double)(Count(l) + Count(r)) > _rnd.NextDouble())
    {
      l.RChild = Merge(l.RChild, r);
      return Update(l);
    }
    else
    {
      r.LChild = Merge(l, r.LChild);
      return Update(r);
    }
  }

  /// <summary>
  /// split as [0, k), [k, n)
  /// </summary>
  public static Tuple<Node, Node> Split(Node t, int k)
  {
    if (t == null) return new Tuple<Node, Node>(null, null);
    if (k <= Count(t.LChild))
    {
      var s = Split(t.LChild, k);
      t.LChild = s.Item2;
      return new Tuple<Node, Node>(s.Item1, Update(t));
    }
    else
    {
      var s = Split(t.RChild, k - Count(t.LChild) - 1);
      t.RChild = s.Item1;
      return new Tuple<Node, Node>(Update(t), s.Item2);
    }
  }

  public static Node Remove(Node t, T v)
  {
    if (Find(t, v) == null) return t;
    return RemoveAt(t, LowerBound(t, v));
  }

  public static Node RemoveAt(Node t, int k)
  {
    var s = Split(t, k);
    var s2 = Split(s.Item2, 1);
    return Merge(s.Item1, s2.Item2);
  }

  public static bool Contains(Node t, T v)
  {
    return Find(t, v) != null;
  }

  public static Node Find(Node t, T v)
  {
    while (t != null)
    {
      var cmp = t.Value.CompareTo(v);
      if (cmp > 0) t = t.LChild;
      else if (cmp < 0) t = t.RChild;
      else break;
    }
    return t;
  }

  public static Node FindByIndex(Node t, int idx)
  {
    if (t == null) return null;

    var currentIdx = Count(t) - Count(t.RChild) - 1;
    while (t != null)
    {
      if (currentIdx == idx) return t;
      if (currentIdx > idx)
      {
        t = t.LChild;
        currentIdx -= (Count(t == null ? null : t.RChild) + 1);
      }
      else
      {
        t = t.RChild;
        currentIdx += (Count(t == null ? null : t.LChild) + 1);
      }
    }

    return null;
  }

  public static int UpperBound(Node t, T v)
  {
    var torg = t;
    if (t == null) return -1;

    var ret = Int32.MaxValue;
    var idx = Count(t) - Count(t.RChild) - 1;
    while (t != null)
    {
      var cmp = t.Value.CompareTo(v);

      if (cmp > 0)
      {
        ret = Math.Min(ret, idx);
        t = t.LChild;
        idx -= (Count(t == null ? null : t.RChild) + 1);
      }
      else if (cmp <= 0)
      {
        t = t.RChild;
        idx += (Count(t == null ? null : t.LChild) + 1);
      }
    }
    return ret == Int32.MaxValue ? Count(torg) : ret;
  }

  public static int LowerBound(Node t, T v)
  {
    var torg = t;
    if (t == null) return -1;

    var idx = Count(t) - Count(t.RChild) - 1;
    var ret = Int32.MaxValue;
    while (t != null)
    {
      var cmp = t.Value.CompareTo(v);
      if (cmp >= 0)
      {
        if (cmp == 0) ret = Math.Min(ret, idx);
        t = t.LChild;
        if (t == null) ret = Math.Min(ret, idx);
        idx -= t == null ? 0 : (Count(t.RChild) + 1);
      }
      else if (cmp < 0)
      {
        t = t.RChild;
        idx += (Count(t == null ? null : t.LChild) + 1);
        if (t == null) return idx;
      }
    }
    return ret == Int32.MaxValue ? Count(torg) : ret;
  }

  public static Node Insert(Node t, T v)
  {
    var ub = LowerBound(t, v);
    return InsertByIdx(t, ub, v);
  }

  static Node InsertByIdx(Node t, int k, T v)
  {
    var s = Split(t, k);
    return Merge(Merge(s.Item1, new Node(v)), s.Item2);
  }

  public static IEnumerable<T> Enumerate(Node t)
  {
    var ret = new List<T>();
    Enumerate(t, ret);
    return ret;
  }

  static void Enumerate(Node t, List<T> ret)
  {
    if (t == null) return;
    Enumerate(t.LChild, ret);
    ret.Add(t.Value);
    Enumerate(t.RChild, ret);
  }
}

/// <summary>
/// C-like set
/// </summary>
public class Set<T> where T : IComparable
{
  protected SB_BinarySearchTree<T>.Node _root;

  public T this[int idx] { get { return ElementAt(idx); } }

  public int Count()
  {
    return SB_BinarySearchTree<T>.Count(_root);
  }

  public virtual void Insert(T v)
  {
    if (_root == null) _root = new SB_BinarySearchTree<T>.Node(v);
    else
    {
      if (SB_BinarySearchTree<T>.Find(_root, v) != null) return;
      _root = SB_BinarySearchTree<T>.Insert(_root, v);
    }
  }

  public void Clear()
  {
    _root = null;
  }

  public void Remove(T v)
  {
    _root = SB_BinarySearchTree<T>.Remove(_root, v);
  }

  public bool Contains(T v)
  {
    return SB_BinarySearchTree<T>.Contains(_root, v);
  }

  public T ElementAt(int k)
  {
    var node = SB_BinarySearchTree<T>.FindByIndex(_root, k);
    if (node == null) throw new IndexOutOfRangeException();
    return node.Value;
  }

  public int Count(T v)
  {
    return SB_BinarySearchTree<T>.UpperBound(_root, v) - SB_BinarySearchTree<T>.LowerBound(_root, v);
  }

  public int LowerBound(T v)
  {
    return SB_BinarySearchTree<T>.LowerBound(_root, v);
  }

  public int UpperBound(T v)
  {
    return SB_BinarySearchTree<T>.UpperBound(_root, v);
  }

  public Tuple<int, int> EqualRange(T v)
  {
    if (!Contains(v)) return new Tuple<int, int>(-1, -1);
    return new Tuple<int, int>(SB_BinarySearchTree<T>.LowerBound(_root, v), SB_BinarySearchTree<T>.UpperBound(_root, v) - 1);
  }

  public List<T> ToList()
  {
    return new List<T>(SB_BinarySearchTree<T>.Enumerate(_root));
  }
}