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: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;

namespace ABC051.C
{
	using static Util;

	public class Solver : SolverBase
	{
		public void Run() {
			int sx, sy, tx, ty;
			ReadInt4(out sx, out sy, out tx, out ty);

			// ↑→ ↓← ←↑→↓ →↓←↑
			var dy = ty - sy;
			var dx = tx - sx;

			var sb = new StringBuilder(10000);
			for (int i = 0; i < dy; i++) {
				sb.Append('U');
			}
			for (int i = 0; i < dx; i++) {
				sb.Append('R');
			}
			for (int i = 0; i < dy; i++) {
				sb.Append('D');
			}
			for (int i = 0; i < dx; i++) {
				sb.Append('L');
			}
			sb.Append('L');
			for (int i = 0; i < dy+1; i++) {
				sb.Append('U');
			}
			for (int i = 0; i < dx+1; i++) {
				sb.Append('R');
			}
			sb.Append('D');
			sb.Append('R');
			for (int i = 0; i < dy+1; i++) {
				sb.Append('D');
			}
			for (int i = 0; i < dx+1; i++) {
				sb.Append('L');
			}
			sb.Append('U');

			WriteLine(sb.ToString());
		}

#if !MYHOME
		static void Main(string[] args) {
			new Solver().Run();
		}
#endif
	}
	public static class Util
	{
		public static int Gcd(int a, int b) {
			if (a < b)
				// 引数を入替えて自分を呼び出す
				return Gcd(b, a);
			while (b != 0) {
				var remainder = a % b;
				a = b;
				b = remainder;
			}
			return a;
		}
		public readonly static long MOD = 1000000007;

		public static string DumpToString<T>(IEnumerable<T> array) where T : IFormattable {
			var sb = new StringBuilder();
			foreach (var item in array) {
				sb.Append(item);
				sb.Append(", ");
			}
			return sb.ToString();
		}

		public static void InitArray<T>(T[] ary, T value) {
			for (int i = 0; i < ary.Length; i++) {
				ary[i] = value;
			}
		}
		public static void InitDP2<T>(T[,] dp, T value) {
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					dp[i, j] = value;
				}
			}
		}
		public static void InitDP3<T>(T[,,] dp, T value) {
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					for (int k = 0; k < dp.GetLength(2); k++) {
						dp[i, j, k] = value;
					}
				}
			}
		}

		public static T Max<T>(params T[] nums) where T : IComparable {
			if (nums.Length == 0) return default(T);

			T max = nums[0];
			for (int i = 1; i < nums.Length; i++) {
				max = max.CompareTo(nums[i]) > 0 ? max : nums[i];
			}
			return max;
		}
		public static T Min<T>(params T[] nums) where T : IComparable {
			if (nums.Length == 0) return default(T);

			T min = nums[0];
			for (int i = 1; i < nums.Length; i++) {
				min = min.CompareTo(nums[i]) < 0 ? min : nums[i];
			}
			return min;
		}

		/// <summary>
		/// ソート済み配列 ary に同じ値の要素が含まれている？
		/// ※ソート順は昇順/降順どちらでもよい
		/// </summary>
		public static bool HasDuplicateInSortedArray<T>(T[] ary) where T : IComparable, IComparable<T> {
			if (ary.Length <= 1) return false;

			var lastNum = ary[ary.Length - 1];

			foreach (var n in ary) {
				if (lastNum.CompareTo(n) == 0) {
					return true;
				} else {
					lastNum = n;
				}
			}
			return false;
		}

		public static bool ReplaceIfBigger<T>(ref T r, T v) where T : IComparable {
			if (r.CompareTo(v) < 0) {
				r = v;
				return true;
			} else {
				return false;
			}
		}
		public static bool ReplaceIfSmaller<T>(ref T r, T v) where T : IComparable {
			if (0 < r.CompareTo(v)) {
				r = v;
				return true;
			} else {
				return false;
			}
		}

		/// <summary>
		/// 二分探索
		/// ※条件を満たす最小のidxを返す
		/// ※満たすものがない場合は ary.Length を返す
		/// ※『aryの先頭側が条件を満たさない、末尾側が条件を満たす』という前提
		/// ただし、IsOK(...)の戻り値を逆転させれば、逆でも同じことが可能。
		/// </summary>
		/// <param name="ary">探索対象配列 ★ソート済みであること</param>
		/// <param name="key">探索値 ※これ以上の値を持つ（IsOKがtrueを返す）最小のindexを返す</param>
		public static int BinarySearch<T>(T[] ary, T key) where T : IComparable, IComparable<T> {
			int left = -1;
			int right = ary.Length;

			while (1 < right - left) {
				var mid = left + (right - left) / 2;

				if (IsOK(ary, mid, key)) {
					right = mid;
				} else {
					left = mid;
				}
			}

			// left は条件を満たさない最大の値、right は条件を満たす最小の値になっている
			return right;
		}
		public static bool IsOK<T>(T[] ary, int idx, T key) where T : IComparable, IComparable<T> {
			// key <= ary[idx] と同じ意味
			return key.CompareTo(ary[idx]) <= 0;
		}
	}

	public class SolverBase
	{
		virtual protected string ReadLine() => Console.ReadLine();
		virtual protected string ReadString() => ReadLine();
		virtual protected int ReadInt() => int.Parse(ReadLine());
		//virtual protected void ReadInt2(out int x, out int y) {
		//	var aryS = ReadLine().Split(' ');
		//	x = int.Parse(aryS[0]);
		//	y = int.Parse(aryS[1]);
		//}
		virtual protected long ReadLong() => long.Parse(ReadLine());
		virtual protected string[] ReadStringArray() => ReadLine().Split(' ');
		virtual protected int[] ReadIntArray() => ReadLine().Split(' ').Select<string, int>(s => int.Parse(s)).ToArray();
		virtual protected void ReadInt2(out int a, out int b) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
		}
		virtual protected void ReadInt3(out int a, out int b, out int c) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
		}
		virtual protected void ReadInt4(out int a, out int b, out int c, out int d) {
			var ary = ReadIntArray();
			a = ary[0];
			b = ary[1];
			c = ary[2];
			d = ary[3];
		}
		virtual protected long[] ReadLongArray() => ReadLine().Split(' ').Select<string, long>(s => long.Parse(s)).ToArray();
		virtual protected double[] ReadDoubleArray() => ReadLine().Split(' ').Select<string, double>(s => double.Parse(s)).ToArray();
		virtual protected void WriteLine(string line) => Console.WriteLine(line);
		virtual protected void WriteLine(double d) => Console.WriteLine($"{d:F9}");
		virtual protected void WriteLine<T>(T value) where T : IFormattable => Console.WriteLine(value);
		virtual protected void WriteGrid(IEnumerable<IEnumerable<char>> arrayOfArray) {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				foreach (var c in a) {
					sb.Append(c);
				}
				sb.AppendLine();
			}
			WriteLine(sb.ToString());
		}

		[Conditional("DEBUG")]
		protected void Dump(string s) => Console.WriteLine(s);
		[Conditional("DEBUG")]
		protected void Dump(char c) => Console.WriteLine(c);
		[Conditional("DEBUG")]
		protected void Dump(int x) => Console.WriteLine(x);
		[Conditional("DEBUG")]
		protected void Dump(double d) => Console.WriteLine($"{d:F9}");
		[Conditional("DEBUG")]
		protected void Dump<T>(IEnumerable<T> array) where T : IFormattable {
			string s = Util.DumpToString(array);
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(s);
			//_writer.WriteLine(s);
		}
		[Conditional("DEBUG")]
		protected void DumpGrid(IEnumerable<IEnumerable<char>> arrayOfArray) {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				foreach (var c in a) {
					sb.Append(c);
				}
				sb.AppendLine();
			}
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(sb.ToString());
			//_writer.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpGrid<T>(IEnumerable<IEnumerable<T>> arrayOfArray) where T : IFormattable {
			var sb = new StringBuilder();
			foreach (var a in arrayOfArray) {
				sb.AppendLine(Util.DumpToString(a));
			}
			// Consoleに出力すると、UnitTestの邪魔をしないというメリットあり。
			Console.WriteLine(sb.ToString());
			//_writer.WriteLine(sb.ToString());
		}
		[Conditional("DEBUG")]
		protected void DumpDP<T>(T[,] dp) where T : IFormattable {
			var sb = new StringBuilder();
			for (int i = 0; i < dp.GetLength(0); i++) {
				for (int j = 0; j < dp.GetLength(1); j++) {
					sb.Append(dp[i, j]);
					sb.Append(", ");
				}
				sb.AppendLine();
			}
			Console.WriteLine(sb.ToString());
		}
	}
}