Problem:
Score : 400 points

Problem Statement

Along a road running in an east-west direction, there are A shrines and B temples.
The i-th shrine from the west is located at a distance of s_i meters from the west end of the road, and the i-th temple from the west is located at a distance of t_i meters from the west end of the road.

Answer the following Q queries:

Query i (1 \leq i \leq Q): If we start from a point at a distance of x_i meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required.)

Constraints

1 \leq A, B \leq 10^5

1 \leq Q \leq 10^5

1 \leq s_1 < s_2 < ... < s_A \leq 10^{10}

1 \leq t_1 < t_2 < ... < t_B \leq 10^{10}

1 \leq x_i \leq 10^{10}

s_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B Q
s_1
:
s_A
t_1
:
t_B
x_1
:
x_Q

Output

Print Q lines. The i-th line should contain the answer to the i-th query.

Sample Input 1

2 3 4
100
600
400
900
1000
150
2000
899
799

Sample Output 1

350
1400
301
399

There are two shrines and three temples. The shrines are located at distances of 100, 600 meters from the west end of the road, and the temples are located at distances of 400, 900, 1000 meters from the west end of the road.

Query 1: If we start from a point at a distance of 150 meters from the west end of the road, the optimal move is first to walk 50 meters west to visit a shrine, then to walk 300 meters east to visit a temple.

Query 2: If we start from a point at a distance of 2000 meters from the west end of the road, the optimal move is first to walk 1000 meters west to visit a temple, then to walk 400 meters west to visit a shrine. We will pass by another temple on the way, but it is fine.

Query 3: If we start from a point at a distance of 899 meters from the west end of the road, the optimal move is first to walk 1 meter east to visit a temple, then to walk 300 meters west to visit a shrine.

Query 4: If we start from a point at a distance of 799 meters from the west end of the road, the optimal move is first to walk 199 meters west to visit a shrine, then to walk 200 meters west to visit a temple.

Sample Input 2

1 1 3
1
10000000000
2
9999999999
5000000000

Sample Output 2

10000000000
10000000000
14999999998

The road is quite long, and we may need to travel a distance that does not fit into a 32-bit integer.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.IO;
using System.Text.RegularExpressions;
using System.Text;
using System.Diagnostics;
using System.Globalization;
using static System.Math;

namespace D
{
	public class Program
	{
		// variables
		int A, B;
		int Q;
		long[] s;
		long[] t;


		void Run(string[] args)
		{
			// main program
			A = Int;
			B = Int;
			Q = Int;
			s = MakeArray(A, i => Long);
			t = MakeArray(B, i => Long);

			foreach (var i in Enumerable.Range(0, Q))
			{
				var x = long.Parse(Line);

				var minL = long.MaxValue;
				{
					var arg_shrine = ArgLower(x, s);
					if (arg_shrine + 1 < A)
					{
						var shrine_r = s[arg_shrine + 1];
						var temple_r = t[ArgNearest(shrine_r, t)];
						minL = Min(minL, Abs(x - shrine_r) + Abs(shrine_r - temple_r));
					}
					var shrine = s[arg_shrine];
					var temple = t[ArgNearest(shrine, t)];
					minL = Min(minL, Abs(x - shrine) + Abs(shrine - temple));
				}
				{
					var arg_temple = ArgLower(x, t);
					if (arg_temple + 1 < B)
					{
						var temple_r = t[arg_temple + 1];
						var shrine_r = s[ArgNearest(temple_r, s)];
						minL = Min(minL, Abs(x - temple_r) + Abs(shrine_r - temple_r));
					}
					var temple = t[arg_temple];
					var shrine = s[ArgNearest(temple, s)];
					minL = Min(minL, Abs(x - temple) + Abs(shrine - temple));
				}

				PrintLine(minL);
			}
		}

		// methods
		int ArgLower(long x, long[] A)
		{
			var leq = 0;
			var g = A.Length;
			while (Abs(leq - g) > 1)
			{
				var mid = (leq + g) / 2;
				if (A[mid] <= x)
				{
					leq = mid;
				}
				else
				{
					g = mid;
				}
			}

			return leq;
		}

		int ArgNearest(long x, long[] A)
		{
			var arg_lower = ArgLower(x, A);
			if (arg_lower + 1 < A.Length)
			{
				if (Abs(x - A[arg_lower]) <= Abs(x - A[arg_lower + 1]))
				{
					return arg_lower;
				}
				else
				{
					return arg_lower + 1;
				}
			}
			return arg_lower;
		}

		// utilities
		static void Main(string[] args)
		{
			new Program().Run(args);
#if DEBUG
			Console.Write("Press any key...");
			Console.ReadKey();
#endif
		}

		/// <summary>
		/// Make an array
		/// </summary>
		/// <typeparam name="T">type of element</typeparam>
		/// <param name="count">number of elements</param>
		/// <param name="input">element generator</param>
		/// <returns>array</returns>
		static T[] MakeArray<T>(int count, Func<int, T> input)
		{
			var array = new T[count];
			for (var i = 0; i < count; ++i)
			{
				array[i] = input(i);
			}
			return array;
		}
		/// <summary>
		/// Make a 2-dimensional array
		/// </summary>
		/// <typeparam name="T">type of element</typeparam>
		/// <param name="count1">size of first dimension</param>
		/// <param name="count2">size of second dimension</param>
		/// <param name="input">element generator</param>
		/// <returns>2-dimensional array</returns>
		static T[,] MakeArray<T>(int count1, int count2, Func<int, int, T> input)
		{
			var array = new T[count1, count2];
			for (var i = 0; i < count1; ++i)
			{
				for (var j = 0; j < count2; ++j)
				{
					array[i, j] = input(i, j);
				}
			}
			return array;
		}
		/// <summary>
		/// Make a 3-dimensional array
		/// </summary>
		/// <typeparam name="T">type of element</typeparam>
		/// <param name="count1">size of first dimension</param>
		/// <param name="count2">size of second dimension</param>
		/// <param name="count3">size of third dimension</param>
		/// <param name="input">element generator</param>
		/// <returns>3-dimensional array</returns>
		static T[,,] MakeArray<T>(int count1, int count2, int count3, Func<int, int, int, T> input)
		{
			var array = new T[count1, count2, count3];
			for (var i = 0; i < count1; ++i)
			{
				for (var j = 0; j < count2; ++j)
				{
					for (var k = 0; k < count3; ++k)
					{
						array[i, j, k] = input(i, j, k);
					}
				}
			}
			return array;
		}

		/// <summary>
		/// Output any value
		/// </summary>
		/// <typeparam name="T">type of value.</typeparam>
		/// <param name="value">value</param>
		[DebuggerNonUserCode]
		static void Print<T>(T value) => Console.Write(value);
		/// <summary>
		/// Output any value on a line
		/// </summary>
		/// <typeparam name="T">type of value</typeparam>
		/// <param name="value">value</param>
		[DebuggerNonUserCode]
		static void PrintLine<T>(T value) => Console.WriteLine(value);
		/// <summary>
		/// Output a line break
		/// </summary>
		[DebuggerNonUserCode]
		static void PrintLine() => Console.WriteLine();

		/// <summary>
		/// Input a word
		/// </summary>
		static string Word
		{
			[DebuggerNonUserCode]
			get
			{
				char c;
				while (char.IsWhiteSpace(c = (char)Console.Read()))
				{
					continue;
				}

				var builder = new StringBuilder();
				do
				{
					builder.Append(c);
				}
				while (!char.IsWhiteSpace(c = (char)Console.Read()));

				return builder.ToString();
			}
		}
		/// <summary>
		/// Input a line
		/// </summary>
		static string Line
		{
			[DebuggerNonUserCode]
			get
			{
				return Console.ReadLine();
			}
		}
		/// <summary>
		/// Input bool
		/// </summary>
		static bool Bool
		{
			[DebuggerNonUserCode]
			get
			{
				return bool.Parse(Word);
			}
		}
		/// <summary>
		/// Input char
		/// </summary>
		static char Char
		{
			[DebuggerNonUserCode]
			get
			{
				return char.Parse(Word);
			}
		}
		/// <summary>
		/// Input byte
		/// </summary>
		static byte Byte
		{
			[DebuggerNonUserCode]
			get
			{
				return byte.Parse(Word);
			}
		}
		/// <summary>
		/// Input ushort
		/// </summary>
		static ushort UShort
		{
			[DebuggerNonUserCode]
			get
			{
				return ushort.Parse(Word);
			}
		}
		/// <summary>
		/// Input uint
		/// </summary>
		static uint UInt
		{
			[DebuggerNonUserCode]
			get
			{
				return uint.Parse(Word);
			}
		}
		/// <summary>
		/// Input ulong
		/// </summary>
		static ulong ULong
		{
			[DebuggerNonUserCode]
			get
			{
				return ulong.Parse(Word);
			}
		}
		/// <summary>
		/// Input sbyte
		/// </summary>
		static sbyte SByte
		{
			[DebuggerNonUserCode]
			get
			{
				return sbyte.Parse(Word);
			}
		}
		/// <summary>
		/// Input short
		/// </summary>
		static short Short
		{
			[DebuggerNonUserCode]
			get
			{
				return short.Parse(Word);
			}
		}
		/// <summary>
		/// Input int
		/// </summary>
		static int Int
		{
			[DebuggerNonUserCode]
			get
			{
				return int.Parse(Word);
			}
		}
		/// <summary>
		/// Input long
		/// </summary>
		static long Long
		{
			[DebuggerNonUserCode]
			get
			{
				return long.Parse(Word);
			}
		}
		/// <summary>
		/// Input decimal
		/// </summary>
		static decimal Decimal
		{
			[DebuggerNonUserCode]
			get
			{
				return decimal.Parse(Word);
			}
		}
		/// <summary>
		/// Input variable length integer
		/// </summary>
		static BigInteger Integer
		{
			[DebuggerNonUserCode]
			get
			{
				return BigInteger.Parse(Word);
			}
		}
		/// <summary>
		/// Input float
		/// </summary>
		static float Float
		{
			[DebuggerNonUserCode]
			get
			{
				return float.Parse(Word);
			}
		}
		/// <summary>
		/// Input double
		/// </summary>
		static double Double
		{
			[DebuggerNonUserCode]
			get
			{
				return double.Parse(Word);
			}
		}

		/// <summary>
		/// Input hex int
		/// </summary>
		static int Hex
		{
			[DebuggerNonUserCode]
			get
			{
				return int.Parse(Word, NumberStyles.HexNumber);
			}
		}
		/// <summary>
		/// Input hex int
		/// </summary>
		static int HexInt
		{
			[DebuggerNonUserCode]
			get
			{
				return Hex;
			}
		}
		/// <summary>
		/// Input hex long
		/// </summary>
		static long HexLong
		{
			[DebuggerNonUserCode]
			get
			{
				return long.Parse(Word, NumberStyles.HexNumber);
			}
		}
		/// <summary>
		/// Input variable length hex integer
		/// </summary>
		static BigInteger HexInteger
		{
			[DebuggerNonUserCode]
			get
			{
				return BigInteger.Parse(Word, NumberStyles.HexNumber);
			}
		}

		/// <summary>
		/// Calculate GCD
		/// </summary>
		/// <typeparam name="T">type of value</typeparam>
		/// <typeparam name="TOp">operator struct of value</typeparam>
		/// <param name="a">first value</param>
		/// <param name="b">second value</param>
		/// <returns>the GCD between <c>a</c> and <c>b</c></returns>
		static T Gcd<T, TOp>(T a, T b)
			where TOp : struct, IDividable<T>
		{
			T x, y;
			return Gcd<T, TOp>(a, b, out x, out y);
		}
		/// <summary>
		/// Calculate GCD
		/// </summary>
		/// <typeparam name="T">type of value</typeparam>
		/// <typeparam name="TOp">operator struct of value</typeparam>
		/// <param name="a">first value</param>
		/// <param name="b">second value</param>
		/// <param name="x">return the coefficient of <c>a</c></param>
		/// <param name="y">return the coefficient of <c>b</c></param>
		/// <returns>the GCD between <c>a</c> and <c>b</c></returns>
		static T Gcd<T, TOp>(T a, T b, out T x, out T y)
			where TOp : struct, IDividable<T>
		{
			T x1 = default(TOp).Zero;
			T x2 = default(TOp).One;
			T y1 = default(TOp).One;
			T y2 = default(TOp).Zero;
			T q = default(TOp).Zero;

			while (0 != default(TOp).Compare(b, default(TOp).Zero))
			{
				var tmp = x2;
				x2 = default(TOp).Subtract(x1, default(TOp).Multiply(q, x2));
				x1 = tmp;
				tmp = y2;
				y2 = default(TOp).Subtract(y2, default(TOp).Multiply(q, y2));
				y1 = tmp;
				q = default(TOp).Divide(a, b);
				tmp = b;
				b = default(TOp).Modulo(a, b);
				a = tmp;
			}

			x = x2;
			y = y2;
			return a;
		}

		/// <summary>
		/// Union-find tree
		/// </summary>
		class UnionFind : UnionFind<Unit, UnitOp>
		{
			/// <param name="count">number of elements</param>
			public UnionFind(int count) : base(count)
			{ }
		}
		/// <summary>
		/// Union-find tree
		/// </summary>
		class UnionFind<TPotential, TPotentialOp>
			where TPotentialOp : struct, IAddable<TPotential>
		{
			/// <summary>
			/// parent indices
			/// </summary>
			readonly int[] Parent;

			/// <summary>
			/// tree rank
			/// </summary>
			readonly int[] Rank;

			/// <summary>
			/// potential
			/// </summary>
			readonly TPotential[] DiffPotential;

			/// <param name="count">number of elements</param>
			public UnionFind(int count)
			{
				Parent = MakeArray(count, i => i);
				Rank = MakeArray(count, i => 0);
				DiffPotential = MakeArray(count, i => default(TPotentialOp).Zero);
			}

			/// <summary>
			/// Get root element
			/// </summary>
			/// <param name="x">element index</param>
			/// <returns>root element index of <c>x</c></returns>
			public int Root(int x)
			{
				if (Parent[x] == x)
				{
					return x;
				}
				else
				{
					var root = Root(Parent[x]);
					DiffPotential[x] = default(TPotentialOp).Add(DiffPotential[x], DiffPotential[Parent[x]]);
					return Parent[x] = root;
				}
			}

			/// <summary>
			/// Get whether two elements belong to the same set.
			/// </summary>
			/// <param name="x">first element index</param>
			/// <param name="y">second element index</param>
			/// <returns>whether two elements belong to the same set</returns>
			public bool Same(int x, int y)
				=> Root(x) == Root(y);


			/// <summary>
			/// Unite two elements
			/// </summary>
			/// <param name="x">first element index</param>
			/// <param name="y">second element index</param>
			public bool Unite(int x, int y)
				=> Unite(x, y, default(TPotentialOp).Zero);

			/// <summary>
			/// Unite two elements
			/// </summary>
			/// <param name="x">first element index</param>
			/// <param name="y">second element index</param>
			/// <param name="potential">potential from <c>x</c> to <c>y</c></param>
			public bool Unite(int x, int y, TPotential potential)
			{
				potential = default(TPotentialOp).Add(potential, Potential(x));
				potential = default(TPotentialOp).Subtract(potential, Potential(y));
				x = Root(x);
				y = Root(y);

				if (x == y) return false;

				if (Rank[x] < Rank[y])
				{
					// Join x to y
					Parent[x] = y;
					DiffPotential[x] = default(TPotentialOp).Negate(potential);
				}
				else
				{
					// Join y to x
					Parent[y] = x;
					if (Rank[x] == Rank[y]) ++Rank[x];
					DiffPotential[y] = potential;
				}
				return true;
			}

			/// <summary>
			/// Get potential difference from root.
			/// </summary>
			/// <param name="x">element index</param>
			/// <returns>potential difference between the element and the root</returns>
			public TPotential Potential(int x)
			{
				Root(x);
				return DiffPotential[x];
			}

			/// <summary>
			/// Get potential difference between two element.
			/// </summary>
			/// <param name="x">first element index</param>
			/// <param name="y">second element index</param>
			/// <returns>potential difference between two element</returns>
			public TPotential Diff(int x, int y)
				=> default(TPotentialOp).Subtract(Potential(y), Potential(x));
		}

		struct Unit
		{ }
		struct UnitOp : IDividable<Unit>
		{
			public Unit Zero => default(Unit);
			public Unit One => default(Unit);
			public Unit Negate(Unit x) => default(Unit);
			public Unit Add(Unit x, Unit y) => default(Unit);
			public Unit Multiply(Unit x, Unit y) => default(Unit);
			public Unit Divide(Unit x, Unit y) => default(Unit);
			public Unit Modulo(Unit x, Unit y) => default(Unit);
			public int Compare(Unit x, Unit y) => 0;
		}
		struct IntOp : IDividable<int>
		{
			public int Zero => 0;
			public int One => 1;
			public int Negate(int x) => -x;
			public int Add(int x, int y) => x + y;
			public int Multiply(int x, int y) => x * y;
			public int Divide(int x, int y) => x / y;
			public int Modulo(int x, int y) => x % y;
			public int Compare(int x, int y) => x.CompareTo(y);
		}
		struct LongOp : IDividable<long>
		{
			public long Zero => 0L;
			public long One => 1L;
			public long Negate(long x) => -x;
			public long Add(long x, long y) => x + y;
			public long Multiply(long x, long y) => x * y;
			public long Divide(long x, long y) => x / y;
			public long Modulo(long x, long y) => x % y;
			public int Compare(long x, long y) => x.CompareTo(y);
		}
		struct FloatOp : IDividable<float>
		{
			public float Zero => 0.0F;
			public float One => 1.0F;
			public float Negate(float x) => -x;
			public float Add(float x, float y) => x + y;
			public float Multiply(float x, float y) => x * y;
			public float Divide(float x, float y) => x / y;
			public float Modulo(float x, float y) => x % y;
			public int Compare(float x, float y) => x.CompareTo(y);
		}
		struct DoubleOp : IDividable<double>
		{
			public double Zero => 0.0;
			public double One => 1.0;
			public double Negate(double x) => -x;
			public double Add(double x, double y) => x + y;
			public double Multiply(double x, double y) => x * y;
			public double Divide(double x, double y) => x / y;
			public double Modulo(double x, double y) => x % y;
			public int Compare(double x, double y) => x.CompareTo(y);
		}
	}

	interface IDividable<T> : IMultipliable<T>
	{
		T Divide(T x, T y);
		T Modulo(T x, T y);
	}
	interface IMultipliable<T> : IAddable<T>
	{
		T One { get; }
		T Multiply(T x, T y);
	}
	interface IAddable<T> : IComparer<T>
	{
		T Zero { get; }
		T Negate(T x);
		T Add(T x, T y);
	}

	static class OperationExtensions
	{
		public static T Subtract<T, TOp>(this TOp op, T x, T y)
			where TOp : struct, IAddable<T>
		{
			return default(TOp).Add(x, default(TOp).Negate(y));
		}
		public static T Sum<T, TOp>(this TOp op, params T[] items)
			where TOp : struct, IAddable<T>
		{
			var sum = default(TOp).Zero;
			foreach (var item in items)
				sum = default(TOp).Add(sum, item);
			return sum;
		}
		public static T Product<T, TOp>(this TOp op, params T[] items)
			where TOp : struct, IMultipliable<T>
		{
			var sum = default(TOp).One;
			foreach (var item in items)
				sum = default(TOp).Multiply(sum, item);
			return sum;
		}
	}
}