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;

class Program
{
    static void Main(string[] args)
    {
        var A = sc.ReadInt();
        var B = sc.ReadInt();
        var Q = sc.ReadInt();
        var S = sc.ReadLongArray(A).ToList();
        S.Add(LINF);
        S.Add(-LINF);
        S.Sort();
        var T = sc.ReadLongArray(B).ToList();
        T.Add(LINF);
        T.Add(-LINF);
        T.Sort();
        var X = sc.ReadLongArray(Q);

        for (int i = 0; i < Q; i++)
        {
            var start = X[i];

            // 開始地点より東にある最も近い神社
            var leftS = Algorithm.LowerBound(S, start);
            // 開始地点より西にある最も近い神社
            var rightS = leftS - 1;
            // 開始地点より東にある最も近い神社
            var leftT = Algorithm.LowerBound(T, start);
            // 開始地点より西にある最も近い神社
            var rightT = leftT - 1;

            var ans = long.MaxValue;
            foreach (var s in new[] { leftS, rightS })
            {
                foreach (var t in new[] { leftT, rightT })
                {
                    var d1 = Math.Abs(start - S[s]) + Math.Abs(S[s] - T[t]);
                    var d2 = Math.Abs(start - T[t]) + Math.Abs(T[t] - S[s]);
                    ans = Math.Min(ans, d1);
                    ans = Math.Min(ans, d2);
                }
            }
            Console.WriteLine(ans);
        }
    }

    struct XY
    {
        public long V1 { get; set; }
        public long V2 { get; set; }
        public XY(long _V1, long _V2)
        {
            this.V1 = _V1;
            this.V2 = _V2;
        }
    }

    static long MOD = 1000000000 + 7;
    static int INF = (int)1e7 + 1;
    static long LINF = (long)1e13+1;
    static Random Rand = new Random();
    static Scanner sc = new Scanner();

    static long Gcd(long a, long b)
    {
        var v = new[] { a, b };
        while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
        return v[0];
    }
    static long Lcm(long a, long b)
    {
        return a / Gcd(a, b) * b;
    }
    static bool IsPrime(long num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false;

        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                return false;
            }
        }
        return true;
    }
    static List<long> PrimeFactors(long n)
    {
        var res = new List<long>();
        var tmp = n;
        for (long x = 2; x * x <= n; x++)
        {
            while (tmp % x == 0)
            {
                tmp /= x;
                res.Add(x);
            }
        }
        if (tmp != 1) res.Add(tmp);
        return res;
    }
    static long[] Divisor(long n)
    {
        var res = new List<long>();
        for (int i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                res.Add(i);
                if (i * i != n) res.Add(n / i);
            }
        }
        return res.ToArray();
    }
    static Result[] ListAll<T1, T2, Result>(IEnumerable<T1> a, IEnumerable<T2> b, Func<T1, T2, Result> f)
    {
        Result[] res = new Result[a.Count() * b.Count()];
        var i = 0;
        foreach (var v in a)
            foreach (var w in b)
                res[i++] = f(v, w);
        return res;
    }
    static IEnumerable<Result> ListAll<T1, T2, Result>(IEnumerable<T1> a, IEnumerable<T2> b, Func<T1, T2, Result> f, Func<T1, T2, bool> s)
    {
        foreach (var v in a)
        {
            foreach (var w in b)
                if (s(v, w)) yield return f(v, w);
        }
    }
    static List<long> Facs = new List<long>() { 1 };
    static long Fac(int n)
    {
        for (int i = Facs.Count; i <= n; i++)
        {
            Facs.Add(i * Facs[i - 1]);
        }
        return Facs[n];
    }
    static long nCr(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        var res = Fac(n);
        res /= Fac(r);
        res /= Fac(n - r);
        return res;
    }
}

class Modulo
{
    public readonly int MOD;
    private readonly List<int> Facs = new List<int>() { 1 };

    public Modulo(int mod = 1000000007) { this.MOD = mod; }
    public int Mul(int a, int b) { return (int)(Math.BigMul(a, b) % MOD); }
    public int Div(int a, int b) { return Mul(a, Pow(b, MOD - 2)); }
    public int Pow(int a, int n)
    {
        switch (n)
        {
            case 0:
                return 1;
            case 1:
                return a;
            default:
                int p1 = Pow(a, n / 2);
                int p2 = Mul(p1, p1);
                return ((n % 2) == 0) ? p2 : Mul(p2, a);
        }
    }
    public int Fac(int n)
    {
        for (int i = this.Facs.Count; i <= n; i++)
        {
            this.Facs.Add(Mul(i, Facs[i - 1]));
        }
        return this.Facs[n];
    }
    public int nPr(int n, int r) { return Div(Fac(n), Fac(n - r)); }
    public int nCr(int n, int r)
    {
        if (n < r) return 0;
        if (n == r) return 1;
        int res = Fac(n);
        res = Div(res, Fac(r));
        res = Div(res, Fac(n - r));
        return res;
    }
}

class Debug
{
    public static void Dump<T>(T[,] array)
    {
        Console.WriteLine();
        var h = array.GetLength(0);
        var w = array.GetLength(1);

        for (int r = 0; r < h; r++)
        {
            for (int c = 0; c < w; c++)
            {
                Console.Write(array[r, c]);
                Console.Write(" ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public static void Dump<T>(T[] array)
    {
        Console.WriteLine();
        Console.WriteLine(string.Join(" ", array));
        Console.WriteLine();
    }
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }

    public string ReadStr()
    {
        return this.Next();
    }

    public char ReadChar()
    {
        return this.Next()[0];
    }

    public int ReadInt()
    {
        return int.Parse(this.Next());
    }

    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }

    public long ReadLong()
    {
        return long.Parse(this.Next());
    }

    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }

    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }

    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }

    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}

static class Permutation<T>
{
    private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
    {
        int N = a.Length;
        if (N == 0)
        {
            perms.Add(stack.Reverse().ToArray());
        }
        else
        {
            var b = new T[N - 1];
            Array.Copy(a, 1, b, 0, N - 1);
            for (int i = 0; i < a.Length; ++i)
            {
                stack.Push(a[i]);
                Search(perms, stack, b);
                if (i < b.Length) { b[i] = a[i]; }
                stack.Pop();
            }
        }
    }
    public static List<T[]> All(params T[] source)
    {
        var perms = new List<T[]>();
        Search(perms, new Stack<T>(), source);
        return perms;
    }
}

class HashMap<K, V> : Dictionary<K, V> where V : new()
{
    private V DefaltValue = new V();
    public HashMap() { }
    public HashMap(V defaultValue)
    {
        this.DefaltValue = new V();
    }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v : base[i] = this.DefaltValue;
        }
        set { base[i] = value; }
    }
}

class Vector<T> : List<T> where T : new()
{
    public Vector() { }
    public Vector(int count, T defaultValue)
    {
        for (int i = 0; i < count; i++)
        {
            this.Add(defaultValue);
        }
    }
}

class PriorityQueue<T> where T : IComparable<T>
{
    public readonly T[] Array;
    public readonly bool Greater;
    public int Count { get; private set; } = 0;

    public PriorityQueue(int capacity, bool greater = true)
    {
        this.Array = new T[capacity];
        this.Greater = greater;
    }

    public void Enqueue(T item)
    {
        this.Array[this.Count] = item;
        this.Count += 1;
        this.UpHeap();
    }

    public T Dequeue()
    {
        this.Swap(0, this.Count - 1);
        this.Count -= 1;
        this.DownHeap();

        return this.Array[this.Count];
    }

    public T Peek()
    {
        return this.Array[0];
    }

    private void UpHeap()
    {
        var n = this.Count - 1;
        while (n != 0)
        {
            var parent = (n - 1) / 2;

            if (this.Array[n].CompareTo(this.Array[parent]) > 0)
            {
                this.Swap(n, parent);
                n = parent;
            }
            else
            {
                break;
            }
        }
    }

    private void DownHeap()
    {
        var parent = 0;
        while (true)
        {
            var child = 2 * parent + 1;
            if (child > this.Count - 1) break;

            if (child < this.Count - 1 && this.Compare(this.Array[child], this.Array[child + 1]) < 0)
            {
                child += 1;
            }

            if (this.Compare(this.Array[parent], this.Array[child]) < 0)
            {
                this.Swap(parent, child);
                parent = child;
            }
            else
            {
                break;
            }
        }
    }

    private int Compare(T a, T b)
    {
        var c = a.CompareTo(b);
        if (!this.Greater)
        {
            c = -c;
        }
        return c;
    }

    private void Swap(int a, int b)
    {
        var tmp = this.Array[a];
        this.Array[a] = this.Array[b];
        this.Array[b] = tmp;
    }
}

class UnionFind
{
    public int[] Parents { get; set; }
    public UnionFind(int n)
    {
        this.Parents = new int[n];
        for (int i = 0; i < n; i++)
        {
            this.Parents[i] = i;
        }
    }
    public int Find(int x)
    {
        if (this.Parents[x] != x)
        {
            this.Parents[x] = Find(this.Parents[x]);
        }
        return this.Parents[x];
    }
    public bool Same(int x, int y)
    {
        return this.Find(x) == this.Find(y);
    }
    public int Union(int x, int y)
    {
        var xroot = this.Find(x);
        var yroot = this.Find(y);
        if (xroot != yroot) this.Parents[xroot] = yroot;
        return yroot;
    }
}
static class Algorithm
{
    static int binarySearch<T>(IList<T> a, T v, IComparer<T> cmp, bool islb)
    {
        var l = 0;
        var r = a.Count - 1;
        while (l <= r)
        {
            var m = (l + r) / 2;
            var res = cmp.Compare(a[m], v);
            if (res < 0 || (res == 0 && !islb)) l = m + 1;
            else r = m - 1;
        }
        return l;
    }
    public static int LowerBound<T>(this IList<T> a, T v, Comparison<T> f) { return binarySearch(a, v, Comparer<T>.Create(f), true); }
    public static int LowerBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, true); }
    public static int UpperBound<T>(this IList<T> a, T v, Comparison<T> cmp) { return binarySearch(a, v, Comparer<T>.Create(cmp), false); }
    public static int UpperBound<T>(this IList<T> a, T v) { return binarySearch(a, v, Comparer<T>.Default, false); }
}