Problem:
Score : 500 points

Problem Statement

On an xy plane, in an area satisfying 0 ≤ x ≤ W, 0 ≤ y ≤ H, there is one house at each and every point where both x and y are integers.

There are unpaved roads between every pair of points for which either the x coordinates are equal and the difference between the y coordinates is 1, or the y coordinates are equal and the difference between the x coordinates is 1.

The cost of paving a road between houses on coordinates (i,j) and (i+1,j) is p_i for any value of j, while the cost of paving a road between houses on coordinates (i,j) and (i,j+1) is q_j for any value of i.

Mr. Takahashi wants to pave some of these roads and be able to travel between any two houses on paved roads only. Find the solution with the minimum total cost.

Constraints

1 ≦ W,H ≦ 10^5

1 ≦ p_i ≦ 10^8(0 ≦ i ≦ W-1)

1 ≦ q_j ≦ 10^8(0 ≦ j ≦ H-1)

p_i (0 ≦ i ≦ W−1) is an integer.

q_j (0 ≦ j ≦ H−1) is an integer.

Input

Inputs are provided from Standard Input in the following form.

W H
p_0
:
p_{W-1}
q_0
:
q_{H-1}

Output

Output an integer representing the minimum total cost.

Sample Input 1

2 2
3
5
2
7

Sample Output 1

29

It is enough to pave the following eight roads.

Road connecting houses at (0,0) and (0,1)

Road connecting houses at (0,1) and (1,1)

Road connecting houses at (0,2) and (1,2)

Road connecting houses at (1,0) and (1,1)

Road connecting houses at (1,0) and (2,0)

Road connecting houses at (1,1) and (1,2)

Road connecting houses at (1,2) and (2,2)

Road connecting houses at (2,0) and (2,1)

Sample Input 2

4 3
2
4
8
1
2
9
3

Sample Output 2

60

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;

class Program
{
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var sc = new Scan();
        // var sc = new ScanCHK();
        var se = new Search();
        int h, w;
        sc.Multi(out h, out w);
        var pw = new long[w];
        var ph = new long[h];
        var wimos = new long[w + 1];
        var himos = new long[h + 1];
        for (int i = 0; i < w; i++)
        {
            pw[i] = sc.Int;
            wimos[i + 1] = wimos[i] + pw[i];
        }
        for (int i = 0; i < h; i++)
        {
            ph[i] = sc.Int;
        }
        Array.Sort(ph);
        for (int i = 0; i < h; i++)
        {
            himos[i + 1] = himos[i] + ph[i];
        }
        long sum = 0;
        for (int i = 0; i < w; i++)
        {
            int m = se.LowerBound(ph, pw[i]);
            sum += himos[m] + pw[i] * (h - m + 1);
        }
        sw.WriteLine(sum + himos[h]);
        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static void swap<T>(IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }
    static string con<T>(string sep, IEnumerable<T> a) { return string.Join(sep, a); }
    static string con<T>(IEnumerable<T> a) { return con(" ", a); }
    static void DBG<T>(params T[] a) { Console.WriteLine(string.Join(" ", a)); }
    static void DBG(params object[] a) { Console.WriteLine(string.Join(" ", a)); }
    static T[] copy<T>(IList<T> a)
    {
        int n = a.Count;
        var ret = new T[n];
        for (int i = 0; i < n; i++) ret[i] = a[i];
        return ret;
    }
}
class ScanCHK : Scan
{
    public new string Str
    {
        get
        {
            var s = Console.ReadLine();
            return s == s.Trim() ? s : "";
        }
    }
}
class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public int[] IntArrWithSep(char sep) { return Str.Split(sep).Select(int.Parse).ToArray(); }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    T cv<T>(string inp)
    {
        if (typeof(T).Equals(typeof(int)))    return (T)Convert.ChangeType(int.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(long)))   return (T)Convert.ChangeType(long.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(double))) return (T)Convert.ChangeType(double.Parse(inp), typeof(T));
        if (typeof(T).Equals(typeof(char)))   return (T)Convert.ChangeType(inp[0], typeof(T));
        return (T)Convert.ChangeType(inp, typeof(T));
    }
    public void Multi<T>(out T a) { a = cv<T>(Str); }
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
class mymath
{
    int Mod = 1000000007;
    public void setMod(int m) { Mod = m; }
    public bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public bool[] sieve(int n)
    {
        var isp = new bool[n + 1];
        for (int i = 2; i <= n; i++) isp[i] = true;
        for (int i = 2; i * i <= n; i++) if (isp[i]) for (int j = i * i; j <= n; j += i) isp[j] = false;
        return isp;
    }
    public List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var isp = sieve(n);
        for (int i = 2; i <= n; i++) if (isp[i]) prs.Add(i);
        return prs;
    }
    public long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[n];
            ret[i][i] = 1;
        }
        return ret;
    }
    public long[][] powmat(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = powmat(A, n / 2);
        if ((n & 1) == 0) return mulmat(t, t);
        return mulmat(mulmat(t, t), A);
    }
    public long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public long[][] trans(long[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[m];
            for (int j = 0; j < m; j++) ret[i][j] = A[j][i];
        }
        return ret;
    }
    public long[] mulmat(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public long[][] mulmat(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mulmat(Bt, A[i]);
        return ret;
    }
    public long[] addmat(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public long[][] addmat(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = addmat(A[i], B[i]);
        return ret;
    }
    public long powmod(long a, long b)
    {
        if (a >= Mod) return powmod(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = powmod(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public long inv(long a) { return powmod(a, Mod - 2); }
    public long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    public long lcm(long a, long b) { return a * (b / gcd(a, b)); }
    public long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        var numerator = new int[r];
        var denominator = new int[r];
        for (int k = 0; k < r; k++)
        {
            numerator[k] = n - r + k + 1;
            denominator[k] = k + 1;
        }
        for (int p = 2; p <= r; p++)
        {
            int pivot = denominator[p - 1];
            if (pivot > 1)
            {
                int offset = (n - r) % p;
                for (int k = p - 1; k < r; k += p)
                {
                    numerator[k - offset] /= pivot;
                    denominator[k] /= pivot;
                }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numerator[k] > 1) ret = ret * numerator[k] % Mod;
        return ret;
    }
}
class Search
{
    // nより大きいの項のindexのうち最小のものを返す
    // n以下の項のindexのうち最大のもの+1を返す
    // そこに挿入
    public int UpperBound<T>(IList<T> a, T n) where T : IComparable<T>
    {
        if (a.Count == 0) return 0;
        int l = 0, r = a.Count - 1;
        while (l < r)
        {
            int m = (l + r) >> 1;
            if (a[m].CompareTo(n) <= 0)
            {
                if (a[m + 1].CompareTo(n) > 0) return m + 1;
                l = m + 1;
            }
            else r = m - 1;
        }
        if (a[l].CompareTo(n) <= 0) return l + 1;
        return l;
    }

    // n未満の項のindexのうち最大のもの+1を返す
    // n以上の項のindexのうち最小のものを返す
    // そこに挿入
    public int LowerBound<T>(IList<T> a, T n) where T : IComparable<T>
    {
        if (a.Count == 0) return 0;
        int l = 0, r = a.Count - 1;
        while (l < r)
        {
            int m = (l + r) >> 1;
            if (a[m].CompareTo(n) < 0)
            {
                if (a[m + 1].CompareTo(n) >= 0) return m + 1;
                l = m + 1;
            }
            else r = m - 1;
        }
        if (a[l].CompareTo(n) < 0) return l + 1;
        return l;
    }
}